Why doesn't my game register as owned?

It's because you bought it as a disc and not digitally through the Xbox store.

I have done this multiple times. I do it every single time I want to play the game, and it still doesn't work. So no it doesn't work, that is why I am demanding a refund or my digital copy be registered to my xbox one

this is a common bug because it shows I still own like 2 360's and such it doesn't register that the device was factory reset it just registers you loged on

Yea, I should have mentioned she doesn't have a console of her own, so she uses mine. The content was downloaded onto her account. So basically the War Games Pass is registered on mine, while the Map Pack itself is registered onto hers. My understanding
is that as long as it's the same console, we're good?

Are the games you own on disc? If so, then that will be why you get the message to subscribe, as the Xbox Series S console is a digital console only, so your disc games will not register on there as being owned, as you need the disc in the console to play the games.