Recently I swapped to Vodafone UK from EE which went through fine. I had a Vodafone physical SIM and swapped to an e-sim. This also went through fine except the Apple watch seemed to get confused. Looking on the Vodafone forum there seems to be a number of circumstances that cause the issue. Below is a screen shot of the error:
Irrespective of which circumstance you see the error code if you open the watch app go to General -> About. If you find EID is blank this should resolve the problem.
Navigate to the following page: https://www.vodafone.co.uk/help-and-information/esim
Click on esim to esim.
Log into My Vodafone
Select your number
Now select Mobile Secondary
The screen will change
Press Apple Watch
Enter the EID number in the box. This can be found in the watch app under General > About
Finally tick the boxes to agree. The esim will be provisioned or more re-provisioned. Now fully close the watch app. Wait a few minutes. Go back into the watch app and the data plan will be active. I did find it showed inactive at first but keep waiting. In my case it took about 5 minutes although it can take 24 hours.
Ignore the message about add a data plan, this does not apply to Apple Watch.