No, it’s not mandatory to have a Nettla Padel Level to use the app.
Court Booking = Levels are not part of regular court bookings.
Private Match = Level span can be set to "Suggested" or "Required" at the moment when the private match is created. Score reporting affects participants levels.
Public Match = Level span is locked at plus/minus 1.00 from the lead booker's level to make sure players who do not know each other have a good game.