One question concerning your Story of adding products at https://supportprofile.apple.com/
When you added your iPhone, did you immediately add your iPad Air - OR - was the adding of the iPad Air from a different session?
Regardless, this sounds like a glitch in the Apple database that can only be addressed BY AppleRealPersons. Start here > Apple Support | Contact
Answer honestly (call it an Apple ID issue) and when making choices, choose "Topic not listed". This should finally produce a page of choices of Contact Options. If it were me, I would choose the telephone over Chat.
Handoff ( feature of Continuity) does not depend on the devices being in your Support Profile.
Our friend seventy one .:| 😉 |:. is talking about your "Product Info" on your Profile ( BIO ) page of ASC - not your SupportProfile - BUT - he IS on the right track concerning 'multiple Apple IDs', although it may not be your doing (the reason I asked the leading question above)
hope this helps
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