AllowedExtensions in Go was the intended single source of truth for library
type file extensions, but it was never synced to the database. This caused
missing extensions like .pdf for manga to be absent from library_types.
- Add SyncAllowedExtensions() to sync Go AllowedExtensions map to DB
- Call SyncAllowedExtensions() from cmd/server/main.go on startup
- Ensure .pdf is included in manga extensions