Hi CelestialSeth and welcome to the forums. I hope you find this a safe place to share anything that's troubling you and that you get some suggestions and support in your journey.
You're in a tough spot but I think you know what you need to do.
You may be "eligible for public housing" and your mother is not but not in the configuration your mother plans.
That is for you to pave HER escape plan.
I understand what she's asking / demanding is pretty much illegal. You can find this out and tell her you're not willing to commit a crime that could destroy your future, before you leave.
Your mother is not your responsibility.
At 22yo you ARE your responsibility.
I had an extremely abusive and controlling mother but have been No Contact for decades. It was by far the most difficult family relationship I've had. Cutting off from the enmeshment she created was extremely hard.
The Police made it physically easy in one fell swoop but emotionally and psychologically the feelings I had from then on for about 5-10y were hard.
I had no idea of the ramifications of calling the police that day but the alternative of staying in contact was NOT an option any more by that stage. I had tried EVERYTHING else. Her actions that day burnt that bridge - or blew it up figuratively speaking. I don't regret it for a nanosecond.
Tbh I would think about my plan first without telling mother. Line all your "ducks in a row" by organising your next place. Even move some things out bit by bit beforehand to a friend's place.
Then sit your mum down and tell her and leave relatively quickly.
You have to be as prepared as you can be for almost any eventuality here.
I'm sure your mother will react angrily and use every word possible to manipulate you eg saying you're abandoning her and possibly that you are cruel etc. She may keep up her attempts to manipulate you for many years. There are techniques & strategies you can learn to protect yourself from this moving forward.
Be resolute and as I said leave quickly.
This takes SO MUCH strength but I know your future self will thank you for making this move.