The automatic switching of Airpods between IPhone and Apple Watch when using Voiceover has never worked as it should and the connection between the Airpods and the Watch could only be decribed as flaky at best. Fortunately, Apple appears to have resolved the problem in IOS 12.1.4 and Watch OS 5.1.3.
I reported this bug to Apple in March 2018 and I though they had decided to ignore me but finally, the bug is gone in the latest versions of IOS and Watch OS.
Once connected to both devices, you can get the Voiceover output from either device simply by touching the screen.
If you've not updated to the latest versions, this is a very good reason to do so.