I believe something weird happens when you trigger them on the ground and then fly off, I know at least once the ground units just would not leave me be after that, like there's no reset at that point.
Running into the building you just broke into works better than trying to flee.
It is the perma which already makes most planets sentinel covered but the more aggressive they are on the planet the worse it is. They can on site start the escalation
I hope OP is able to survive long enough to fight off all the waves they send out before giving a pillar location away. 
Ugh, then yeah you gotta dig a hole or just run, though like flying to the space station and reloading there would probably reset them. I am not sure if it's intentional or a glitch, but it definitely seemed to be a thing that they would not give up after I fled in the ship.
It's not even that difficult. Just go into the building and stand there. They'll deactivate almost immediately. As long as you're not in a hostile/aggressive sentinel environment they won't bother you when you leave.
If no building just run in one direction. They'll eventually give up.
If in your ship summon and enter the Anomoly. Instant deactivation.
I know the feeling, awhile ago I came back after over a year off and was really surprised by how much more often I had to deal with Sentinels.
If you just lay on your thruster button while leaving orbit of the planet you pissed them off on, you should be able to escape them in something like 4-5 seconds, and then you can go right back to what you were doing on that planet.
if you can break it down and solve the riddle theres some good rewards, like getting a V1, V2, and V3 pass before reaching the Anomaly station. Just make sure you have a circuit board thing in your inventory when you go in because you only get one attempt.
Haven't played in years, I don't think cloaks were available when I played on ps4. Can't imagine that i played all the way to the center and got the plat without finding a cloak... or maybe I just don't remember it. Many games ago 🤷♂️ but I shall look out for one on my new journey
I am guessing you may have shot the door on a manufacture facility. Once the door is shot open there should be a terminal inside that will shut the sentinels down.
You can shoot the doors off with your ship. Avoid the sentinels. Then you can sit in there until they shut down. If you parked your ship right you can hop back in and blast off before they get crazy. That being said if it is an aggressive sentinel planet all bets are off. They will not let up. Rather than pulsing you can call and land in the anomaly usually. Another option would be find the pillar there and turn off all the sentinels on that planet. Shoot the three smaller structures and you can usually unlock and disable the space cops (aka atlas' mistake) pretty quick.
The easiest way to escape is on the ground in an exocraft. They quit chasing pretty quickly. Getting into your ship these days... well you saw that.
What you may not know is that you can completely shut down sentinels on a planet now as well. You can either kill all 5 waves or find a sentinel tower and defeat a much smaller force there. They eventually reactivate, but I've heard varying times on how long, anything from simply leaving the planet to three days. Still, quite useful if you want to explore a aggressive sentinel planet.
If you sit in the building instead of running they usually search and deactivate. Just stand off to the side and not right in front of the door. You can also try and outrun them on foot or exocraft. It’s harder to do that on a high/aggressive sentinel planets though.
I don't think the sentinels were less relentless as much as it was a genuine limitation back then where transitioning between planets and space would get rid of your wanted level.
The Outlaws update 2 years ago made it so pirates and sentinels don't lose your track when you go to a planet, they stay on your ass pretty much how you'd expect them to. It used to be a major exploit in evading combat that got patched out.
(Though you can still hide in buildings or summon the space anomaly.)
A PD save instantly makes sentinels more aggro as well as more common.
If you aggro them on the ground, your options are hide (either dig a hole & seal it or get into a building if one's around) or run. Just pick a direction and get away. Their LoS is shit, so they're not hard to shake off. Don't take off in your ship as that just calls in the fighters.
If you do aggro them airborne or fly off, get to the space station or call in the anomaly and land. That ends the alert.
I miss how it used to be. If you killed the sentry before it called for backup, combat ended.
Now combat never ends and just escalates forever unless you run far and fast enough. That was not a gameplay improvement IMO.
"Nothing warned me that trying to open this door in the middle of nowhere would be a galactic crime"
That not a crime at all, it is you that is the crime ;-)
I believe something weird happens when you trigger them on the ground and then fly off, I know at least once the ground units just would not leave me be after that, like there's no reset at that point. Running into the building you just broke into works better than trying to flee.
It is the perma which already makes most planets sentinel covered but the more aggressive they are on the planet the worse it is. They can on site start the escalation I hope OP is able to survive long enough to fight off all the waves they send out before giving a pillar location away. 
Didn't even break it, barely scratched it. Don't even have a weapon yet, just the mining tool
Ugh, then yeah you gotta dig a hole or just run, though like flying to the space station and reloading there would probably reset them. I am not sure if it's intentional or a glitch, but it definitely seemed to be a thing that they would not give up after I fled in the ship.
In space, land on a space station, that interrupts the sentinels.
Or the Anomaly. Just summon it and land if you’re far enough into the game to do so.
‘nade the doors quickly and if Skynet gives chase dig a tunnel down and hide out until the heat dies
I relearned that just now, actually after grabbing a grav ball... they didn't like that
If an object shows an icon with stars, then it will generally result in sentinels coming first you. The more stars the higher the wanted level
It's not even that difficult. Just go into the building and stand there. They'll deactivate almost immediately. As long as you're not in a hostile/aggressive sentinel environment they won't bother you when you leave. If no building just run in one direction. They'll eventually give up. If in your ship summon and enter the Anomoly. Instant deactivation.
I was able to do just that on the next encounter after obtaining blaster to actually open the door this time.
Skynet??? i’m gunna go massacre sentinels now, while pretending they’re enemy Terminators. thank you for this insight, Traveller.
Once you make it to space just summon the anomaly and land on it. When you leave everything will be chill again
I know the feeling, awhile ago I came back after over a year off and was really surprised by how much more often I had to deal with Sentinels. If you just lay on your thruster button while leaving orbit of the planet you pissed them off on, you should be able to escape them in something like 4-5 seconds, and then you can go right back to what you were doing on that planet.
if you can break it down and solve the riddle theres some good rewards, like getting a V1, V2, and V3 pass before reaching the Anomaly station. Just make sure you have a circuit board thing in your inventory when you go in because you only get one attempt.
The cloaking device helps you hide while you put distance between yourself and the sentinels.
summon the anomoly if you want to get out of it.
If you have the Phantom cloak on your weapon, you can use that to hide. For 1-star Sentinel encounters, it'll outlast the search countdown.
Oo phantom cloak, that def sounds new.
It's been in the game for a while now, it's a secondary tool like the Personal Forcefield
Haven't played in years, I don't think cloaks were available when I played on ps4. Can't imagine that i played all the way to the center and got the plat without finding a cloak... or maybe I just don't remember it. Many games ago 🤷♂️ but I shall look out for one on my new journey
I am guessing you may have shot the door on a manufacture facility. Once the door is shot open there should be a terminal inside that will shut the sentinels down.
Sometimes. Secure facilities use to be a go to spot for all sorts of upgrades.
You can shoot the doors off with your ship. Avoid the sentinels. Then you can sit in there until they shut down. If you parked your ship right you can hop back in and blast off before they get crazy. That being said if it is an aggressive sentinel planet all bets are off. They will not let up. Rather than pulsing you can call and land in the anomaly usually. Another option would be find the pillar there and turn off all the sentinels on that planet. Shoot the three smaller structures and you can usually unlock and disable the space cops (aka atlas' mistake) pretty quick.
The easiest way to escape is on the ground in an exocraft. They quit chasing pretty quickly. Getting into your ship these days... well you saw that. What you may not know is that you can completely shut down sentinels on a planet now as well. You can either kill all 5 waves or find a sentinel tower and defeat a much smaller force there. They eventually reactivate, but I've heard varying times on how long, anything from simply leaving the planet to three days. Still, quite useful if you want to explore a aggressive sentinel planet.
If you sit in the building instead of running they usually search and deactivate. Just stand off to the side and not right in front of the door. You can also try and outrun them on foot or exocraft. It’s harder to do that on a high/aggressive sentinel planets though.
Did that my 2nd encounter with a building. 1st time I didn't get the door open, had no weapon then, just ran to ship
When running from sentinels in ship change to speed settings and roll out. You'll nearly always outrun them.
I don't think the sentinels were less relentless as much as it was a genuine limitation back then where transitioning between planets and space would get rid of your wanted level. The Outlaws update 2 years ago made it so pirates and sentinels don't lose your track when you go to a planet, they stay on your ass pretty much how you'd expect them to. It used to be a major exploit in evading combat that got patched out. (Though you can still hide in buildings or summon the space anomaly.)
You have to destroy the door to get in...
A PD save instantly makes sentinels more aggro as well as more common. If you aggro them on the ground, your options are hide (either dig a hole & seal it or get into a building if one's around) or run. Just pick a direction and get away. Their LoS is shit, so they're not hard to shake off. Don't take off in your ship as that just calls in the fighters. If you do aggro them airborne or fly off, get to the space station or call in the anomaly and land. That ends the alert.
Should be fine if you enter it, they can't see you even if they follow.
I miss how it used to be. If you killed the sentry before it called for backup, combat ended. Now combat never ends and just escalates forever unless you run far and fast enough. That was not a gameplay improvement IMO.
Yeah, it's a little much. Like I'd you interact with an object slightly, the entire galactic police shouldn't show up instantly.
"Nothing warned me that trying to open this door in the middle of nowhere would be a galactic crime" That not a crime at all, it is you that is the crime ;-)
If I break the door and go in the are stuck searching for me and give up If you go in the air call and board the anomaly and they’ll disappear after
-break into secure facility -shocked when someone calls popo
I didn't break in, though. literally knocked on the door (with the butt of my multitool)