Thanks for the new video! Much clearer now.
My guess, from seeing that, is that the NAS is constantly sending file-change events for the file, which is causing the metadata panel to keep refreshing the tags it displays.
If you turn on Preferences / Miscellaneous / Advanced: no_external_change_notify and the problem stops, that would support my theory.
You could also do the Debugging steps in the Changes to folders are not being detected guide; if you do, I bet you'll see an endless stream of lines saying the PDF has changed.
We've seen this a couple of times before where just reading the file attributes or other metadata from a file, without modifying the file at all (or even opening a write handle to it), can generate a change event on some setups. The change event causes Opus to refresh the file, reading it again, which then (wrongly) triggers another change event.
It can be caused by shell extensions (e.g. Microsoft themselves ship an email shell extension with Windows that really modifies the file each time it's asked to read it), but if that were the case it would probably affect all of your devices.
If the NAS is doing that, it's something to report to Synology so they can fix it in a firmware update. (I have a feeling one of the NAS vendors had a similar problem in the past where reading file attributes triggered a change event. Not sure which one it was, but that was years ago and hopefully has been fixed by now.)