Can you enable auditing of Dataverse system settings including the "block unmanaged" one?
Yes you can! Just enable auditing on the table called “organization”. Many per environment settings you can edit at admin.powerplatform are stored in this table.
You can also use this knowledge to help you automate your updates to system settings rather than doing them per env as a manual activity. The organization table will always contain a single row and you can update it like any other row.