Schroedingers_Kater:
Also, I have a pro micro, and the button-press to keyboard-mapping works like a charm (albeit, not wirelessly yet).
This caught my eye.
A pro-micro can pretend to be a keyboard by virtue of its USB connection. There is no simple way to convert that to wireless. When you have (say) a wireless keyboard it is the dongle (or whatever) that is plugged into the PC that appears to the PC to be a keyboard.
What should work is to use two Arduinos. Have a pro-micro connected by USB and communicating by wireless with another Arduino. That would be functionally similar to a wireless keyboard.
...R