Somehow Firefox opens outside my screen on a "separate one" every first time I launch the app, and the only way to switch between "screens" is to open a new tab through task manager or launch a program that was previously active to switch back to previous "screen". It is also impossible to switch between opened windows on different "screens" using gestures on the touchpad or "Alt" + "Tab".

This took me down a rabbit hole of the multi-desktop feature. Could you take a look at this section of a video showing how to move things between desktops. Once you empty out an unwanted desktop, I think you can close it using the X button at the upper right of the empty desktop.

https://youtu.be/ZUttvpJMq8E?si=bFjhrVflLA8R_V97&t=211

*Edit* Later he says if you are viewing a desktop you can press Ctrl+WindowsKey+F4 to merge it into the previous desktop, so the windows of desktop 2 would move into desktop 1. That sounds faster but I've never tried any of this myself.

I have tried renaming the file called "xulstore.json" to "xulstore.old" or deleting it entirely, this didn't resolve the issue.

I think it's a Windows issue, but since you are already familiar with where Firefox stores screen position (xulstore.json), you could open the file in a text editor and sanity check the first group of settings (this is mine at the moment):

"main-window":{"screenX":"7","screenY":"0","width":"462","height":"126","sizemode":"maximized"}

Does yours show peculiar values for the first two parameters -- position -- or the second two parameters -- size? (I don't know why the height is so short on mine. Annoying.)

Oh my God. Thank you so much! Yes, the problem was indeed in multi-screen feature of Windows. I prefer not to clog interface, so I removed most of the buttons from the taskbar. Because of this I didn't see task view button and couldn't formulate search request correctly.