I see the same issue with a Watch Series 9. There is no switch to enable developer mode in the Privacy & Security menu (WatchOS 10.0.1), and the Watch also does not show up in Xcode. Developer mode works as expected on iPhone.

I was also struggling with this problem for a week and tried nearly every link I found on Google... So I had a perfectly working setup where I could run and debug my app on the Watch. Then I got a new Watch, but could not enable developer mode and hence did not see the Watch in Xcode. The setup: Xcode 15.0, WatchOS 10.0.2, iOS 17.0.2, macOS 14.0, iPhone 15 Pro, Watch Series 9. Here is what worked in the end: Unpair Watch from iPhone. Unpair the iPhone in Xcode. Switch off development mode on iPhone. Turn off iPhone. Delete all Xcode settings as described in https://developer.apple.com/forums/thread/705846. Delete Xcode, empty trash. Restart Mac. Restart iPhone. Download Xcode 15.0. Unpack, open Xcode 15.0. Open project (no elegible devices connected to My Mac). Connect iPhone to Mac via USB cable. Select "Trust computer" on iPhone. iPhone shows up in Xcode, but asks that developer mode to be enabled. Enable developer mode on iPhone. Restart iPhone. iPhone shows up in Xcode as development device. App starts successfully on iPhone. Close Xcode. Disconnect iPhone from USB cable. Pair Watch to iPhone as new watch (no restore from backup). Wait until all Watch apps have been installed. Open Xcode. Connect iPhone with USB cable. Watch shows up in device overview in Xcode, but asks that developer mode to be enabled. Developer mode finally appears on the Watch. Enable developer mode on Watch. Restart Watch. Start Watch app in Xcode. Prompt to register device appears. Register device. The app starts on the Watch. I wish there was a less invasive way to solve the problem, but I found none and this worked for me.