With an Axiom (or any midi controller) you can program each button, pad, slider etc to output most types of midi information.
I have set the pads to midi note numbers (using notes which are unlikely to be needed). Note numbers 0-7
I have set the buttons to output midi cc information. It was necessary to set the buttons to use a CC Value + command. I have set these as send a range of 0 - 1, so only a single increment triggers.
With those set it’s simply a case of assigning the midi controllers in Dorico.
For my personal mapping I have put the note values from Semibreve to demisemiquaver on the pads (6) using 7th and 8th pad to send dot and tie. My buttons are assigned to navigation L, R, U, D, Triplet On, Triplet Off, Force Note Length, Resolution -, Resolution +
I will get around to assigning a few more when I get a minute, but these have improved the workflow for now.
It’s also important to save the setup on the Axiom, because it can store many presets of controllers.
Hope this helps