Thanks for providing so cool product! I'm a heavy user so facing one issue:
It seems that this issue is similar with #2491.
Can you please try to re-sync your webhook? https://docs.readthedocs.io/en/latest/webhooks.html#resyncing-webhooks
For detecting new branches we need new permissions.
Also, this can be achieved by triggering a new build.
visit the integration detail page and follow the directions for re-syncing your repository webhook.
I cannot find the directions for re-syncing webhook in integration detail page. I also confirmed that the config page in GitHub side has no direction either.
I'll attach screenshot of RTD site. Do I need to delete and recreate webhook?

Your webhook wasn't created when you imported the project, that's why. You can add new permissions from the gihub side. These permissions (events) https://docs.readthedocs.io/en/latest/webhooks.html#github
Thanks! I've updated config in GitHub side, and watch coming builds to confirm how it works.
Was the problem solved?
I've confirmed that new branch is listed in the RTD's version page. However old branch (already removed from GitHub) is still listed. I hope this has no problem for my app.
I will confirm with my users, to make sure we can close this issue. Thanks for your waiting!
It seems that no problem has been reported recently. Thank you, I will close this issue :)
Old branches that are marked as active in RTD, don't get deleted. That's by design.
Only inactive ones are deleted