You dont need the install preserved, you need the login session preserved. I doubt that it’s even possible

Ah ok. So its not so much the current files that you want to retain, but the ability to receive files locally through sync, when someone else elsewhere makes a change?

Sounds a bit like not wanting to remove the Netflix app because its logged in with the unknown password of an ex.

This is the most important piece of information. You should edit the post and/or title to make this more clear.

I would back up all the important files you need before you change anything.

Well, that makes a huge difference to the meaning of the question.

I don’t know, but maybe the login is held in a dotfile such as ~/.dropbox or maybe in ~/.config/dropbox or similar, and just backing up that (not to Dropbox!) would be enough to restore being logged in on a different system.