My watch appears paired, except for in the app
I noticed I wasn’t getting text or calls on my watch & when I open the app, it appears as if my watch is not paired. However, when I try to pair it, it doesn’t work.
Apple Watch Series 8
If you don't get notifications, messages, or calls on your Apple Watch, your Apple Watch and iPhone might not be connected. When your devices disconnect, the red iPhone icon
or the red X icon 
appears on your watch face. You can also check your connection in Control Center. When your Apple Watch connects again, the green iPhone icon 
appears. For more info and troubleshooting tips see:
If your Apple Watch isn't connected or paired with your iPhone - Apple Support