This just keeps coming back. It's one week away from the first anniversary of a certain console tip on We Suck Less:
Peter Chamberlain wrote:If you use Fusion today, and need a Fusion Studio feature, buy Fusion Studio (dongle) and that dongle will also work on DaVinci Resolve 15.
If you don't need something in Fusion Studio today, and would prefer the activation key, purchase DaVinci Resolve Studio.
Fusion 16 is capable of running off a Resolve dongle as far as I remember, but Fu9 obviously doesn't have that new code (because that's not how they roll).
It's annoying there is such ambiguity about what runs what, and the communication about it is lacking.
That said, I have heard that people have successfully exchanged their Resolve dongles for Fusion ones. Hope BMD support can sort something out for you.