I can't recall connecting any mini split systems that needed more than 20 amp breaker, in fact most if all only needed a 15 amp breaker.
I've done a larger scale VRF system before with multiple compressors some on 60 or even 80 amp three pole breakers, but the zone valves and room air handling units had low enough current draw that there were multiple units on a single 15 amp 208 volt single phase circuit. Signaling was all via twisted pair at low voltage and interconnected every controlled component of the entire system with this same two wire network, each component had a network address and basically only responded to commands on the system that contained it's address in the command.