Dictation is part of Siri. If Siri is having issues using your wi-fi network, dictation could also be effected.
Two troubleshooting steps are:
• Power off the watch and then the iPhone. Next, Turn on the iPhone first followed by the watch. This sequence of shutting down and turning on the devices sometimes can fix a lot of issues including the dictation feature.
• Force restarting the Apple Watch can be helpful. Press and hold both the side button and the Digital crown until you see the Apple logo. Let the watch start up on its own and then you can check if you are still experiencing tech issues on the watch.
Beyond that, try dictation using a different wi-fi network. Or contact Apple.
Get Support -
https://getsupport.apple.com/
ASC - Late 2012 Mac mini, macOS 10.14.6; Watch, series 5 GPS/cellular, watchOS 6.2.8; iPad Air 2, ipadOS 13.6.1; iPhone 8+, iOS 13.6.1; TV 4th Gen, tvOS 13.4.8; HomePods, audioOS 13.4.8 and Airport Express w/ Airplay 2