With docker you get the DB engine, in the case of Plausible is Clickhouse, and the data is up to you (is in the Docker volumes). I needed to migrate from machine A to machine B, and while redeploying Plausible engine was a breeze, I was unable to take a full backup of the Clickhouse data, and following their docs I could only get the backup file, but was unable to restore it. Then, IIRC, I did data dumps, one per table, but some dumps loaded cleanly while others refused, losing some details. OTOH, backuping and restoring the Postgres data was as easy as it Docker wasn't involved. Sumup: the problem was not Docker or Plausible, but Clickhouse.
