I'm currently using Thunderbird on my PC and my laptop.
Is there a way to sync the read-status of the newsgroup messages between my two Thunderbird installations?
You can exchange, e.g. via a claud storage the file newsrc, defining read status of articles. It is a plaintext file.
You can find its location and name in every TB instance in the Usenet account settings - Server settings - newsrc: location.
Edit: In case the newsrc filename do not much, you can unify them and set the new name in the account server settings. OR, you can perform the newsrc file renaming in a syncing script, e.g. during automated sync procedure.
See more in my 2014 discussion about the same topic. mozilla.support.thunderbird › Syncing NNTP account between TB instances
In case of the TB instances are crossplatform, like Linux and Windows, make sure each platform receives the expected line ending - LF for Linux, CRLF for Windows. Especially Windows are picky and do not like LF EOL in this case.
You can use utilities dos2unix and unix2dos, converting EndOfLine formats between Windows and Linux/Unix. There are Windows binaries and there are Linux utils for the same ( but I have already hit the 2 links limit for the post )