Should I quit my job at my current company because of the lack of work and flimsy hiring practices?

I'm a recent comp. Sci graduate and have been working as an AI engineer since my senior year. I was initially hired as a trainee with the promise of a promotion to full time once I graduated which was about 6 months from then. The terms of the timeline were only verbally stated so my contract was not time period bounded. It's been 3 months since I graduated and there had been no update on the promotion until today. I received an offer today but the terms felt odd to me. It said that I would have to work a 3 month probation period during which I was not eligible to the benefits of the package, and my employment could be terminated at any point without need to provide a reason for termination.

Another problem with the role is the work is very unchallenging. The best way to explain it is that I doubt this experience could benefit me in any applications I might make to other companies for this role. Based on the standard requirements for junior AI engineers, I would not measure up in most cases. Before I got the offer today I had mostly made up my mind to quit and take my chances with temporary unemployment. I've also been doing other internships because I literally have no work here for months on end.

The last point is the company practices for hiring and project management. I keep hearing talk of poor finances and tough times but the company spendings don't reflect that to me. My team lead went so far as to say that layoffs could be coming soon. There are people in my team who have stuck in the same role for over 3 years, which makes no sense for the amount of work they actually do. And I've heard from a lot of former employees that this company fires people without notice often and I'm inclined to believe that.

I also might have to relocate because my mom needs me for a medical emergency and that is the reason I'm in doubt about accepting this offer too cuz I can't take PTO and if they don't allow me to work remotely then it'll be a big problem for me.

So my question is, should I continue here until I find something better or just quit rn given the work, reputation and my personal circumstances.

Any advice?