Photos app, v 5.0 (121.17.170) does not show the "Photos" tab under "Library"

These two are from the Foto-app that does not show the 'Foto tab'.

These two are from the MacBook Pro where the Foto-tab does show.

And I just tested putting it back to English. Nope, nothing happened (see screenshot).

The Catalina I installed on the MacMini was a clean install.

Leoni, can't I, somehow, remove the Photo's app, and install it again?

I read your response again, and now I understand. You installed a new copy of Photo's from the original disk. Nice work, but it did not work. So, I will install Catalina entirely.

Well, did a clean install on my Mac mini. No, didn't solve it. Perhaps this was there from the beginning...

I checked but my system isn’t accidentally in save mode.

I just tested you suggestion by making a new user, with no Apple ID. Nothing's changed.

Then the problem is system wide and it will not help to trash preferences files from your user account.

Have you installed any new software on the Mac Mini, that is not installed on your other Mac? There may be third party system extensions or custom fonts, that are causing this. If third-party system extensions are the problem, it should vanish, when you restart the Mac in Safe Mode. See: Use safe mode to isolate issues with your Mac - Apple Support

if the problem goes away in Safe Mode, try to isolate it.

Then check the list of things disabled by Safe Mode and compare it to the hardware of your mac. Perhaps your Macs graphics has natively the limited graphics option, that are causing the problem: "Safe mode in OS X Leopard v10.5 or later also disables accelerated graphics. " Which graphics card is installed on your mac? My Mac has an Intel UHD Graphics 630 1536 MB installed and my guess is, the menu items vanishes, if the accelerated graphics is not available. This would then only apply to certain mac models.

Also one of these changes might apply:

Starting your Mac in safe mode does the following:

• Verifies your startup disk and attempts to repair directory issues, if needed
• Loads only required kernel extensions
• Prevents startup items and login items from opening automatically
• Disables user-installed fonts 
• Deletes font caches, kernel cache, and other system cache files

It might be a missing font or a wrong kernel extension.