No, I didn't really find a fix for it. But I uninstalled Teams, deleted all cache and local files that I could find, installed Teams again, but the issue was still there for a while. Then after a day or two, it slowly went away, less and less chats were affected. Funny thing is, even the online web version of Teams was affected, so it's really an issue on their end, not my local cache.
Overall it took about a week to get it fully working again.
This is a big issue, microsoft should fix it asap.