If physical intimacy is important and it’s important for you in a marriage, then ending it might be the only solution. Obviously cheating wasn’t a solution as it’s typically not the way to improve one’s situation.

Maybe there are some ways to improve financial situation by getting second jobs, downsizing etc

If divorce could cause you to not be able to stay in the US, maybe the right person to ask for advice is immigration lawyer? Or any lawyer for that matter, they could give you suggestions.

You asked if you should stay or you should move on, but then you said you can’t separate neither legally nor unofficially and really can’t move on. So it sounds like you have to stay anyways.

Or were you really asking if you should have other relationships while married (since you can’t get divorced)? You could, if your spouse is on board. But you’d have hard time finding women willing to entangle with a married man.

So what exactly are your alternatives to just staying unhappily married and trying to improve your situation?