I need this framed in every room so I don't make that mistake again

And do not park in or near the driveway, you will get blocked in then you'll have to spend half an hour (at best) finding random people and having them move their car so you can leave

Way ahead of you: they can't even see my car from the house. This way, it's possible to vanish long before anyone figures it out.
Show up late so you can leave early.

Go by public transport so you can have a drink to help get through it and if that isn't enough you can still leave.

I wish my home town had public transportation
- it's taxi time

The real pro move is to carpool with like minded people with a kid.

"Oh, I would love to stay but John's son is so fussy and they are my ride. It was great seeing you, we should do this again"

"It was great seeing you again"
"but... You just got here five minutes ago"
"SO great..."
Caution, this only works reliably with parents with younger kids, the older their youngest the less this works lol
- I dunno, teens and adult children can be fussy too.

Having a dog helps too as you have a plausible excuse to leave and a conversation topic.

Just say you gotta shit then leave without saying goodbye to anybody.
- Just ~~say you gotta~~ shit on the front porch, then leave without saying goodbye to anybody.
But then I have to pay and care for a dog. I'll just not put myself in either situation.
- Neighbors' dog that you're taking care of for the week¹ works as well.
  ¹ no actual neighbors' dog required

Public transport is nice too "ah sorry I've gotta catch my bus, it was lovely to see you bye!"

Bring snacks secret ones.

Protip: do this but do NOT bring a whiskey flask or edibles. Yeah, it may take the edge off, but you may need your wits about you.
- The edibles are for when you have to stay the night ☺️

Then you can deal with the "It might be rude for me to leave now. I'll just stay a little longer." "Okay, just 15 more minutes." "Okay, at the top of the hour, I'll leave." "Someone just got here, so I'll stay another half hour so they don't think I'm leaving just because they got here."

Irish good byes are the best way to go.
- My family usually get an "okay I'm gonna go now. I'll see you later" and that's about it.
  But by then they can tell I've had enough of people today and want to leave so they're never surprised.
  And if anyone wants to think I left because they arrived, so be it. I am not the shepherd of my family's emotions.
  I can't just leave without saying anything though. Not unless they pissed me off.
- One of my favorites
- It's tough for us midwesterners to do that.

I guess I'm lucky since I enjoy spending time with my family and haven't had to consider things like in op

No matter where I am, I always have a sketch in my head as to what "leaving" would be like. How long it would take in total, then for each leg:

Stand up
Pick up coat
"Welp."
Put on coat
Walk to door
Open door
Make one last witty comment before closing door behind me
Walk to car
Open car door
Sit down
Foot on brake
Turn key to START
When engine is running, release ignition key to ON position
Seatbelt
Steering wheel
click Reverse
Release brake
Rear view while backing up
Steer onto street
Apply brake
click click Drive
GO

This is obviously different if I'm somewhere where I have not taken my own car and have to depend on alternate transportation, whether that be:

Public transit
Catch a ride with someone else
Rideshare/taxi
Walking
Rental bike/e-bike/e-scooter
Canal boat
Slip-N-Slide
Pneumatic tube
Quantum tunnelling
Window
Magic[k]
Hiding until everyone else leaves
Go to sleep

I've got a pretty nice system.
1: PANIC
B- Go
You may notice there's no conversation before the final step. This is because my anxiety doesn't allow me much talking until I can decompress.
It's worked so far.

This is the mid-to-final stage in the family trauma galaxy-brain meme:

I'm screwed up, and it's my fault
I'm screwed up and it's my family's fault
My family screwed me up because they're also screwed up
My family screwed itself up, from long before I was born
If I stick around, I'm gonna get more screwed up

Also, if you look around and think about it, you may be able to identify which family members are practicing limited/no contact. They may be screwed up too, but at least they're aware of it.