How to manage updates on production as web agency

1: Update the GitHub private repo with your changes
2: Write an email to the customer sysadmin and ask to sync in staging and later production
3: Wait 2 weeks and do another ping about it
4: The sysadmin later will do that
5: In the meantime there is a security update of your CMS and a lot of plugins to update
6: Try to update from the CMS panel and there are no write permission
7: Cry a lot and write another email to go back to point 2