Oh, sorry I forgot about that. Long story short: by enabling access to the rest of your user's home directory, Thunderbird thinks that there's no profile created (because it searches for a profile folder in a few dedicated places in order).
We can fix that easily. Close Thunderbird, and open up the terminal again. First, make some backups, just in case:
cp -r ~/.var/app/org.mozilla.thunderbird/.thunderbird ~/thunderbird_old
cp -r ~/.thunderbird ~/thunderbird_new
Two new folders should appear in your home directory. Then, delete the one that was just created accidentally by enabling access through Flatseal:
rm -rf ~/.thunderbird
And create the symbolic link, or shortcut:
ln -s ~/.var/app/org.mozilla.thunderbird/.thunderbird ~/.thunderbird
You should now be able to launch Thunderbird and use your account as it was previously setup.
If everything seems to work fine — and only if everything seems to work fine — you can delete the two folders that appeared in your home directory named "thunderbird_old" and "thunderbird_new".
For reference: