Are purchases I make in this app available across all my Apple devices? For example, if I purchase Premium for iOS, am I also able to access Premium features on the macOS version of the app?
Purchases are shared as long as you use the same Apple ID or another Apple ID in your family library.
There is no macOS version of Hue Essentials. If you are using an M1 Mac then you can install the iPad version of Hue Essentials. I think purchases should be shared with this app as well.
See also the following for more information: All about orders and refunds
OK, thanks very much for the clarification – I saw that M1 Macs are supported, and assumed macOS, but iPadOS makes sense too.