It is just a dead CMOS battery. So the clock had the wrong time, which in turn also causes the log entries to have the wrong time and date. Simply replace the battery. It is most likely of the CR2032 type.

Syncthing is neat, but you shouldn’t consider it to be a backup solution. If you accidentally delete or modify a file on one machine, it’ll happily propagate that change to all other machines.

No, it is not dumb. My second link was just an example to a fix of one particular laptop where this issue occurred. I mentioned all this just to point to the issue that might be causing your problem. I’m afraid this probably does not fix it for you. Maybe it has been fixed with a more recent kernel. You could check which version you are running (by running uname -a from a terminal) and maybe update to a newer one if your distro allows that. Alternatively you could downgrade the kernel to a version before this issue was introduced (a 6.10 kernel should work okay). Of course downgrading should only be a stop-gap solution.

Yes. Apparently the issue happens with both internal mics and mic connectors where you attach your own mic. The seconds link I provided points to a fix for a specific laptop that fixes a non-working internal mic.

It is probably due to this change in the Linux kernel. That broke analogue microphone inputs on lots of systems. After that change, there were quite a few additional patches fixing those problems on individual systems (e.g. this one), but there are still lots of broken setups around. I have no idea what the original change was about exactly. It appears to have broken more things than it has fixed, but what do I know.