Those are typically the database files and are normally located in the your Gramps User Directory, for Linux systems that would typically be in the .gramps/grampsdb folder.
The “hex-named” is the Gramps generated “handle”. Trivia: the handle can be decoded to the extract the date the Tree was created.
After you make a backup of the folder, point your Gramps Preferences for the “Family Tree” tab’s “Database path” to that folder. (Remember the old path.) The dialog from “Family Trees → Manage Family Trees…” should list more trees in the old BSDDB format… which would need to be converted to SQLite:
