Are you currently using a version from the repositories of your Linux distribution?
Try the Firefox version from the official Mozilla server:

https://www.mozilla.org/en-US/firefox/all/

@FredMcD

Indeed, I am using Firefox from the default openSUSE repository.

For a while I used the openSUSE Mozilla repository ( http://download.opensuse.org/repositories/mozilla/openSUSE_Tumbleweed/ ) which is slightly ahead where I saw this first and then switched back to the main distribution repository. While tumbleweed used to be unstable in the distant past, it is nowadays mainly a very up to date rolling release distribution. (Less stable than Leap, but nevertheless very robust overall even it there are some beta version, such as for example LibreOffice 7 right now.)

The 64-bit executable for Linux from the Mozilla website works fine. - Though this isn't a longterm viable solutionm however it might help to pinpoint the issue.

In the Mozilla repo, I have 78.0.2-5.5-x86_64 (link above) which unfortunately still has the same issue... (I get the Window I posted in the screenshot in the first post.)

@FredMcD

Indeed, I am using Firefox from the default openSUSE repository.

For a while I used the openSUSE Mozilla repository ( http://download.opensuse.org/repositories/mozilla/openSUSE_Tumbleweed/ ) which is slightly ahead where I saw this first and then switched back to the main distribution repository. While tumbleweed used to be unstable in the distant past, it is nowadays mainly a very up to date rolling release distribution. (Less stable than Leap, but nevertheless very robust overall even it there are some beta version, such as for example LibreOffice 7 right now.)

The 64-bit executable for Linux from the Mozilla website works fine. - Though this isn't a longterm viable solutionm however it might help to pinpoint the issue.

In the Mozilla repo, I have 78.0.2-5.5-x86_64 (link above) which unfortunately still has the same issue... (I get the Window I posted in the screenshot in the first post.)

Ah:

I remained on v 78.0.2-5.5-x86 from the opensuse Mozilla repository

I deleted .cache/mozilla/ and I got my Firefox back again. So I do not know what caused the issue (seems related to a specific version and the cache?), but it seems ti works again at least.

Could have been a problem with the startup caches that are located in the ~/.cache location.

@cor-el

Maybe. Though I might have tried clearing the .cache before already, so I do think this is linked to a specific version. Unfortunately I never looked at the original version when I first saw the issue on the mozilla repo and just switched over to the official repository...

You didn't show the full error message in the screenshot in case there was some text that explain what is a wrong, but this kind of error is usually a problem with corrupted files or a problem with a specific Firefox locale that is missing some strings.

@cor-el

This was all I would get. No other error messages, no Windows resizing, just this little Windows with a bit of cryptic red text.

I am not sure what can go wrong with the locale... I am pretty insistent on picking UK English when given a choice, but it is plain English, so that shouldn't cause any issues...