Since you've reinstalled via the appcenter, it's deleted the previous backups, but they're not gone just yet, they're kept for 30 days for situations like this.
I'd suggest running snap saved in a terminal, you'll see a list of ID's, one of which should be associated with the Joplin that was removed. Something similar to e.g.,:
$ snap saved
Set Snap Age Version Rev Size Notes
30 go 25d5h 1.10.7 3092 387B -
30 vlc 25d0h 3.0.6 770 882kB -
31 vlc 529ms 3.0.6 770 882kB auto
With the Set/ID, you can run sudo snap restore $ID and it'll restore the content of the older installation. The correct ID will likely have auto as a note, because that's something snap has made for you as a last resort, most people don't make sets manually and would rarely see manual package manager level backups.
Once that's done, go into $HOME/snap/joplin-desktop/common and take a copy of the backups that run daily before the conflict corruption spreads into those too. With the JEX's, you'd be able to restore your notes, assuming they didn't restore anyway from the snap command above (which should in theory return you to the exact point before you uninstalled, which would unfortunately still be with the conflicts).
Whilst I don't expect the conflict issue is caused by the snap itself, with those JEX files, you can reimport the data into e.g., the AppImage or Flatpak releases if you'd rather avoid the snap for now.
I wouldn't be able to help diagnose the underlying cause of the conflict issues, but a good place to start would be acquiring the Joplin log files and seeing what they've got to say, I'd not assume the snap to be causing conflicts by virtue of being a snap itself, so if there's an underlying issue, that issue is probably still there in your other devices and needs sorting.
Ultimately deleting everything and reimporting can be a good if heavy handed solution, but it'd be across all your devices, whereas hopefully some experts on the sync logic here might be able to offer a more precise approach. But your immediate concern should be grabbing the JEX files whilst they're still usable.
There would have been a second level of backup of the previous version of the snap (likely 3.1.23) and I'm unsure whether this snap restore will unfortunately bring you that one back, purely as I've never tried; but, if the restored version 3.1.24 is unusable and the common folder doesn't help, you could finally try sudo snap revert joplin-desktop to try get 3.1.23 back, which reverts not just the app version but the entireity of its database to the point just before the upgrade process began (3.1.24 was released Monday, so these backups could be up to 5 days old). If that doesn't work, you can take a look in $HOME/snap/joplin-desktop/ anyway. The numbered folders represent revisions, the lower number will be the older release, and if it's there, you can browse it, peek at hidden files, and copy the raw Joplin config folder and paste it separately. (snap revert essentially repoints back to this older folder automatically).