In an automation triggered by Issue created, I tried adding For: Parent branch to set a "Global ID" custom field to {{issue.key}}. The branch seems not to be in the log at all.
Before I tried this, I tried to find a trigger for a separate automation for the Epic when a child is created, but I couldn't identify such a trigger.
Issue created automation

More of the automation

Automation log
Note that the Edit issue in the log seems not to be from the For: Parent branch, but the next edit that is further down. The displayed issue key (the Story key) seems to support this.
