Hopefully this helps someone...
I just had to deal with this nightmare again, after an hour on the phone educating another Apple Support &AppleCare rep about this we finally got a bit of a quasi-solution.
To link the AppleCare annual plan to my AppleID they eventually directed me to
this secret page to add the serial number and agreement number from the Apple Pro Display to my account.
The display now shows up in my subscriptions much like AppleCare+ for an iPhone or Mac does, see the image below.
Ultimately it still isn't listed under My Devices where it should be, but I can make this compromise work.
You'd think Apple would have a solution for this in 2025 for one of their current products.
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