Apple Watch series 6
Apple Watch is paired perfectly to my phone, but shows a endless search for Bluetooth devices when trying to connect other devices.
Apple Watch Series 6, watchOS 8
If it is endless for more than a few minutes the software might have locked up or stalled. I suggest try a Forced Reset to reboot the watch, press and hold both the Digital Crown and the Side Button together until the Apple appears, then release and wait. See if that clears the problem.