Following this with interest. Do you have several of these buttons, from the same source, just the one, or several from different makes?
I’ve been thinking on similar lines, per twitter, and wonder about changing the device firmware to choose a different key. Reason for this is I want several buttons to each have different functions. Another advantage is it could work on PC and Mac easily.
Your way is very neat for Pi control and way easier to repeat under Linux, so I will reproduce it for my boiler automation as a boost button.

Will order 3 from the same vendor and see if I can also get at the firmware via those UART tags. Having control over either side of the mapping would be superb.