In a previous job I had a "kick the server" button configured from a Termux integration that would automatically SSH in, punt some logs my way and kill some commonly misbehaving services we didn't control, and then failing that reboot. As long as my phone was on the VPN it was generally a one-click triage.

For a couple of weeks I'd automated myself out of on-call by hooking that to an automation that fired every time I got paged. I wasn't brave enough to keep it going in the long term, but it was the best two weeks of sleep I had at that place.