The Control Center moved from a swipe up to the flat oval side button (see picture)

Use Control Center on Apple Watch - Apple Support
Do a quick press and release of the flat oval side button to bring up the Control Center. You will find the iPhone ping icon in the Control Center list of services.
DO NOT hold the button, as that will bring up Emergency Services display.
Settings -> Accessibility -> Side Button Click Speed
can be used to adjust the press and release timing, so you can reliably bring up the Control Center every time you try. Adjusting this option is also useful when using the Apple Pay double press and release. I like the Slow setting, while my Wife likes Slowest.
You may also find the following page useful:
What’s new in Apple Watch and watchOS 10 - Apple Support