Step back a moment, and lets be methodical about it.
Does Apple TV+ work on your iPad? Is any Apple TV+ content playable there?
That would confirm that the Apple TV+ subscription is active, and that Family Sharing is functional. And you can then make it work on other devices.
To access Apple TV+ on the web, you have to manually sign in in the top right corner, with your same Apple ID account as used for Family Sharing. Once signed in, the Sign-in button icon would change into a circular account icon.
Additionally, when not signed in, you would see ‘Start Free Trial’. Once signed in, you would have ‘Play Episode’.
Ignore the (auto-play) previews.
Select an episode tile below that to start watching.
or select a 1 year free trial.
The year offer is for new eligible Apple devices only. Users without that, would get a much shorter trial period.