Success! I finally contacted Apple Support via phone. The first rep couldn't help - just kept wanting me to update to absolute latest OSs, e.g 15.1.1 vice just 15.1! Called again and got a knowledgable rep named Heather. After checking lots of stuff, it turns out that in order to use an iPad with a Watch for Fitness+, you have to have the Home app loaded on your iPhone!
As soon as I downloaded Home (make sure it's the one from Apple) from the App store, everything worked just fine! The reason is that you can't "pair" the iPad to the Watch because the Watch is paired already to the iPhone. Instead you need to use the iPad as an accessory, the same as you would if you bought special Apple remote devices such as smart lights.
Thank you to everyone who tried to help.