Automations creates a record in a child table and show the automation owner as the new ""created by/record owner"" for the child record.

Whoever last modifies an Automation becomes the new owner.  The modification can be a trivial change to the Description at the top right or the comments at the bottom right.

If you have the Automation being triggered on a record change (as opposed to a Schedule), then you do have access to the [Last Modified] and [Date Modified] of the trigger record.  That can be written to the record(s) being modified  and leverage in some way  in a formula user field.  



For example, if the most recent of the [date modified] = [date modified by Automation], then use the [Last Modified of who triggered the edit] field, else use the native [date modified]