Apple doesn't need to break backward compatibility to block Beeper, they just need a way to fingerprint traffic from Beeper which is going to be trivial unless Beeper finds a 100% on-device solution.
Even then, it'll still be pretty easy because Apple has trillions of interactions with Apple devices to analyze and compare against Beeper.
Beeper on the other hand has far fewer users, who by now likely expect a bad experience. Beeper can be way more agile.