Hi,
you're right that it is indeed
amenity=kick-scooter_parking.
(this tag was coined before "kick_scooter" was proposed as the vehicle type)

All the *_rental, *:rental, and *_parking tags use the vehicle type in the key and therefore should be "kick_scooter_parking=*". 
There is AFAIK no other key of this group with a dash in it. Having a dash in the main key is very uncommon.