Watches currently can only be fully Bluetooth sync’d to iPhones ONLY.
You DO NOT need the iPhone Watch app to use an Watch with the Fitness+ app on an iPad.
Your iPad needs more that just the app.
Here are the requirements needed to use the Fitness+ app and Watch with a iPadOS compatible iPad.
Your iPad needs to be updated to the latest iPadOS version, currently, at iPadOS 15.7.
You need a compatible Watch ( series 3 or later ) updated to its latest watchOS version.
No options.
To be able to use AND continue to use the Fitness app, Apple keeps forcing its Fitness users to keep upgrading/updating these devices to maintain compatibility/connectivity of all of these devices.
The Fitness+ app will ask to automatically link the Watch to your iPad/ Fitness+ app, after the download of the Fitness+ app from the iOS App Store.
See the iPad/iPhone instructions here below.
How to start a workout.
Tap the link below.
How to use Apple Fitness+ - Apple Support
Also, make sure all connected Apple devices are using the same Apple ID/password account information.
In addition, there is no TV mirroring of the Fitness+ app, using iPad, currently.
Currently there is no direct AirPlay/screen mirroring from an iPad to any other compatible smart TV or smart device using AirPlay2.
Apple, currently has ONLY made the mirroring/AirPlay 2 feature available to owners/users of an actual Apple TV box.
Best of Luck to You!
With all that I have stated, I would Contact Apple support, via the contact support link located at the upper right hand corner of every Webpage of these Apple support communities OR by installing and using the Apple Support app found in the iOS App Store.
Tap the iOS App Store link below.
https://apps.apple.com/us/app/apple-support/id1130498044
See if Apple support tells you if you need the Watch, now, or not, using Apple Fitness+ with an iPad.
I keep getting conflicting information about this.
And as far as I am aware, you still cannot AirPlay the Apple Fitness+ app or the videos from an iPad, either, but my info may also, be in error.
Best of Luck to You!