I had 'Immovable windows' quite a few times when I first got the Pi 4.. So regularly that it annoyed me enough to make a text file about how I fixed it in case it happened again.
Can I ask you please to give a detailed description of what you mean when you write "immovable windows" because I've never seen anything like that happen and I've been using multiple desktops on PIs for as long as I can remember.
My experience might be similar enough.
Since I began running Raspbian from SSD instead of microSD, that, and several other annoying problems have gone away.
The actual problem for me (and maybe petr2) was, as they explained in about the 3rd or 4th post, clicking the mouse on the titles bar and dragging does nothing. Clicking the Close, Max/Restoreand Min icons on the title bar do nothing. ALT+ Mouse click and drag does nothing and trying to drag a side or corner or side to resize does nothing. Also there was no menu response right clicking on any part of a frozen window.
Right click the Desktop and choose Desktop Preferences.
Click the Defaults tab (on the right end of tab bar)
Click on Set Defaults.
I found I could click the Defaults for the screen size I was already using and it would work ok. BUT - I would lose a couple of small thing like custom font sizes and single click to open files.
But it was a hell of a lot easier than reinstalling the OS (like I did the first half dozen times).
Again, it has not happened since I started running Raspbian from the SSD.
It also never happened when running Manjaro from the same microSD card I had when I had the problem with Raspbian.
For me it's part of testing a P4B as a possible "replacement" for my Gigabyte Brix box - one desktop is for the "main m/c" the second for remote connections (PuTTY terminal or VNC) to other m/c's more often than not other Pi's. The only "niggle" is that, at the moment, all the desktops have to have the same background.
@ FTrevorGowen I got my Pi 4B because I use a BRIX BACE-3150 instead of my big computers for day to day stuff and wondered about the Pi as a replacement. Now the only time I turn the BRIX on is to print stuff, because there are still no print drivers for the Pi. (NOT the fault of the Pi People).
The Pi 4 is just more comfortable to use in so many ways, and once I managed to get a different picture on each Desktop wallpaper I was much happier
Like you, I use the different wallpaper on each desktop as a quick visual cue..