Hearing other appliances in dedicated line

My guess would be arcing. Those appliances may be on one circuit and there is a loose wire connection at either a receptacle or the branch circuit breaker. Call an electrician and describe the problem.

Loose connection on the audio system circuit or on other lines?

could be either or both, check your panel connections for tightness

Is your audio system breaker on the opposite leg (phase) as these appliances? That could help.

So big a deal was my discovery years ago that some of the ground wires were not tight inside my 200 amp breaker box Stereophile published my letter to them about it. Taking proper precautions,I hand tightened every wire inside that breaker box. My issue wasn’t clicks but rather, hum. Never heard any anomalies again.