I can't locate and ring iPhone using Apple Watch's Find My

This flat oval side button (see picture)

Use Control Center on Apple Watch - Apple Support

DO NOT hold the button, as that brings up Emergency services. Rather a quick press and release.

Settings -> Accessibility -> Side Button Click Speed

“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 timing of 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.

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.

Are you asking about this icon in the Control Center?

In watchOS 10, the Control Center is now accessed by pressing the Side Button once.

M1 Mac mini, macOS 14.2;  Watch, series 7 GPS/cellular, watchOS 10.2; iPad Pro 2nd Gen, iPadOS 16.7.3; iPhone 12 Pro, iOS 17.2; TV 4th Gen, tvOS 17.2; HomePods, audioOS 17.2 and Airport Express w/ Airplay 2

The latest watchOS is version 10.x. I am not sure about the Find My issues that you are having.

You can locate and hear your missing iPhone by going to the Control Center and tapping on the right icon. The Control Center on your Apple Watch which you were once able to get to by just swiping up on the face of your Apple Watch. In watchOS 10, swiping up from the bottom of the watch screen opens the Smart Stack – a new screen with rectangular widgets showing you information at a glance.

Axel F.