Sorry my messy question. I tested this a little more and found
1. If User starts workflow from entity forms "Run workflow" button, then the Workflow runs with Users credentials as you say.
2. If the workflow is started when "Record field change" then it is runs with workflow Owners credentials.
3. If I change the workflow to real-time workflow then i got option to choose "Execute as the user who made changes to record"
So nr. 3 solves my problem. I still wonder if there still is possiblity to run background workflows as "Execute as the user who made changes to the record"?