As you have already seen, an extension can include pretty much any database object, including regular tables. Such tables can be populated when the extension is installed or updated. They can also be modified by users during the life cycle of the database.
By default, backup tools such as pg_dump do not include extension objects to be dumped, since they can always be recreated from the extension scripts. However, if the user changes the data in the extension tables, this data will be lost (or, more accurately, it will not be automatically backed up).
One solution could be to back up this data manually, but this is tedious work. PostgreSQL allows us to indicate that a specific table must be included into the backup, even if it belongs to an extension. This is done by invoking the pg_extension_config_backup() special function with the following arguments...