the "share your location" doesn't really have anything to do with airtags, or tracking the location of airtags either belonging to you or others.
it's more about where find my thinks YOU actually are. If you share your location with others, with the way you have it set up it will show you as wherever your iPad is.
It might have to do with the "travel with" feature, If find my thinks you are where your iPad is, then technically your tag is not "with you" when you're out and about with just your phone. So others might get the "unaccompanied tag traveling with you" notification that they shouldn't get if you and your tag are traveling together.
In theory you shouldn't get that notification since the tag is registered to your account, but with the fairly obvious holes (family sharing), who knows if that slipped through too.
I'm not sure if any of your devices actually "see" the tags, unless you're in precision find mode. The tags send out the pings, and any apple devices that hear them forward those pings to apple. It's very possible that the location of your tags on all your devices is pulled from apple's servers as opposed to it actually being generated locally. I'm not sure how the encryption for find my works, but there's a good chance your devices don't even know that the ping is coming from one of your own tags.
Ultra Wideband only applies in precision find mode. And it will work no matter which device is sharing your location. It should have no impact on reporting locations to find my if your device doesn't have it.