I drag my Project Panel to my left monitor and manually resize it to fill the screen. I click 'Save Changes to this Workspace'. Next time I open that project, or ANY project, I have to go through this routine again. EVERY SINGLE TIME. And yes, I have tried to disable 'Import Workspace from Projects'. As a matter of fact, just in case I was thinking in reverse on this setting, I've tried it both ways for several years to no avail.
Even Kevin-Monahan typed this last year on a similar post..."I'll move this into the Bugs forum. It's time this worked for dual screen monitor setups more reliably. Upvoted. Sorry for the frustration."
This has been a long standing bug and has been reported many times both here in the forum and in Bug Reports...but nothing EVER gets done. Guess Adobe is too busy with AI intergration at the moment, and prior to that, they were more interested in 'Text-based Editing', and prior to that...etc., etc.
You've got some local issue there. There are millions of daily users, many of us with two, three, or four screens. I run four on my main desktop, have for years now. Typically run an additional even with my laptop.
I don't have any such issue, and being pretty active here and on other forums, this isn't happening a lot, shall we say?
So ... first thing to comment on, is you cannot save changes to a 'built-in' workspace. You have to create a new, named workspace to save any changes to it. You don't list that step above, so I don't know if you created a new workspace or not.
Past that, more details is always better. What's your OS and hardware,. especially the monitors, and how do you feed a signal to them?