Executing a form automation
The System app has an "execute automation" action that can be used for one automation to execute another automation:
But when the executed child automation contains a form, that child automation must be turned on in order for form submissions to be processed.
To do this, use the "executed by automation (instant)" System app trigger as the trigger in the child form automation:
Now the child form automation can be left turned on so its form(s) will receive submissions and the child automation will only perform processing when executed by its parent automation(s).