It looks like Github branch rulesets allow setting a bypass for specific app integrations! This should allow my Github app to avoid making a branch, PR, and auto-merging... which would be nice eventually!
First time giving rulesets a try
I'm exploring using Github Apps for w2z instead of fine-grained personal access tokens (PATs). Replacing PATs every 90 days is a bit tedious. Eventually the app flow should give a better experience.