My Apple Watch 6 keeps switching to the “SOS” face without any prompt

Getting the press and release timing just right can be an issue. You can make it more reliable by changing: Apple Watch -> Settings -> Accessibility -> Side Button Click Speed After changing this I never accidentally get the Emergency Services display. “Side Button Click Speed” can adjust the press and release timing, so you get the Control Center display every time. Adjusting The "Side Button Click Speed" is also useful for Apple Pay’s double press and release. There is “Default” (sub second press and release timing needed), “Slow” (up to a second between press and release), and “Slowest” (up to 2 seconds between press and release). I like the “Slow” setting. And as I said, I do not accidentally get the wrong display. NOTE: Slow and Slowest settings do not mean you have to wait a full second or 2 seconds between press and release. It just means you do not need to be super fast.