The database files should be accessible. On my production server they are at /var/discourse/shared/standalone/postgres_data, yours may be in a similar place.
I’d suggest doing a FULL backup of the system to another server before going further, especially all the directories that are under a ‘discourse’ directory.
In the absence of a current (enough) backup, I’d create a new server using a more current version of ubuntu (and thus docker) and then copy all the directories under the discourse trees to it, including all the postgres files. (I haven’t had to do this on a discourse server yet, but I’ve administered postgres databases for 20 years and if the database files are intact that aids in recreating/rebuilding things.)
Has it been a while since this system was updated? If the answer to that question is ‘yes’ there could be complications with trying to copy existing files under the discourse directories to a new server, because that’s really not the right way to do it; a discourse backup has a lot more than just the postgresql database files in it. (This is why I try to do a backup before even a small upgrade, although I’ll admit I don’t always do it.)
Your latest discourse backup is probably in a directory similar to this one:
/var/discourse/shared/standalone/backups/default