On the left, here's what I see when I check if the new (old) Android phone knows about my app purchase. Obviously, it does know that I bought this app. So I do the "upgrade" as suggested, and when I get to the last step, they're about to charge me again, that's where I stop.
If this were just for $5, I'd just buy it. But, if I want to further upgrade, or buy some other application and have it on both (or multiple) devices, I'd like to figure this out now. The older phone is running Android 6, and the new one is Android 11.
Screen shots from added device (Samsung Galaxy Note 4).