> It can handle the full 15 amps of the circuit safely.

OP would need a more beefy relay for an AC unit. 20A minimum, but honestly a 30 or 40A relay would be warranted as AC units have a pretty large "spike" when they turn on which generally exceeds the amp rating of their circuit. It's short enough to not trigger a circuit breaker, but it's something to be aware of when designing things like relays.

I'm fairly certain those exist. The "click" that a car charger makes is a commuter (sp?) (basically a relay) connecting the car to voltage. Mine handles 40 amps.