macbook pro – Apps installed from App Store do not work

I have a 15-inch MacBook Pro Mid 2010 running on a fresh install of the last supported macOS version (High Sierra 10.13.6). I know this is really old, but except for the battery (which I removed from the laptop) it is still a great machine. Everything works fine except apps installed from the App Store do not start (downloading and installing works fine). Immediately after double-clicking the app, I get the following error message:

The Unarchiver quit unexpectedly. Click Report to see more detailed information and send a report to Apple.

Again, this happens with all apps from the App Store (not just “The Unarchiver”).

Strangely enough, apps installed not from the App Store work just fine. I tried installing Microsoft Teams, Discord, and Minecraft, and all apps are starting and working normally.

I digged around a bit and found out that maybe this problem is related to app signatures not working for the App Store somehow. For example, I verified the signature of “The Unarchiver” using the following command in my terminal:

$ codesign --verify --verbose /Applications/The
In architecture: x86_64

Signatures for apps downloaded outside the App Store are OK:

$ codesign --verify --verbose /Applications/Googe
Google valid on disk
Google satisfies its Designated Requirement

Does anyone know what’s going on here? I already contacted Apple Support, but they don’t know either and they won’t escalate this issue because both my MacBook and macOS High Sierra is too old (and therefore unsupported).

Also, this issue doesn’t seem to be related with Many OS X app store apps are listed as “app” is damaged and can’t be opened, which gives a different error message.