Did you ensure jobqueue has been processed, i.e. it is empty?

Yes, I just checked with api.php?action=query&meta=siteinfo&siprop=statistics again: The job queue is definitely empty but the problem is there.

Actually I just realized that because of this bug the translation progress indicators also show wrong information (for most of the languages it says "0% translated" but actually they're completely translated)

Any help on how I can fix my running system would also be welcome!

You can try action=purge in Special:MessageGroupStats or Special:LanguageStats.

I tried that in different ways but it didn't help, situation is still the same. Any other suggestions on how to fix that?
(PS Sorry for my slow response)

Well, as a final measure you could empty the translate_groupstats table where language != '*';

Samdvorak, did this fix itself?

For what it's worth, the translated page most recently moved on Meta-Wiki (17 days ago) doesn't exhibit the issue.

Yes, I emptied the table translate_groupstats and that fixed it.
Now also the page translation progress indicators (I mean those "100% translated" tooltips in the "Other languages" section) are correct again.
This seems to be the workaround solution whenever inconsistencies made their way into translate_groupstats