A little while back I helped someone alter icons but that was in Windows Os. Mind you it's all probably same files etc within the actual program. https://support.mozilla.org/en-US/questions/1429417

That number 1 in green circle. The unread count is gathered from info located in the 'folderCache.json' file - located in profile. In Windows it's a red circle. I recently had an annoying discrepancy. Number did alter but it was always a given number incorrect. I discovered there was a folder from an account which had been set up as a pop account and then modified to be a deferred account using Local Folders. I discovered that the original pop account data was still in the 'folderCache.json' file. It was locating an unread mail. "totalUnreadMsgs" : 21,

If I exited Thunderbird. I could then have 'edited' that line to say: "totalUnreadMsgs" : 0 and then saved the file, but I was concerned it wouldonly rewrite itself again. Instead I located the actual profile data - renamed the mbox file and moved it to Local Folders account folder. then renamed folderCache.json to force a new build.

I did create a bug report for it. https://bugzilla.mozilla.org/show_bug.cgi?id=1916455

Worth taking a look at that link because I included info on how to debug to find out where that number info was coming from.

Maybe it's something like a relic bit of data from when profile was stored in Snap default location, because the Flatpack would have installed in a different location. Did you manually move the profile folder after the reinstall?

It would be interesting and helpful if you could follow the debug info and then post what you found in the error console. In the same way I posted info in that bug report.