Summary:

The ability to select an Actor for automations in Studio is not currently supported. Studio operates as a separate app from Jira's built-in automation engine, so the Actor configuration — which allows rules to run as the Automation for Jira default actor — is only available in the native Jira automation experience (Jira → Project Settings → Automation or global automation).

Workaround: Recreate or migrate the automation rules into native Jira Automation, where the Actor field can be configured.

Suggestion:
I would like to suggest Studio team bring back the Actor field in the new Studio Automations experience, restoring parity with the native Jira Automation settings, where users can select the Automation for Jira default actor.