I used to moonlight as a harpsichord tuner, and I didn't know anyone in the field or any piano tuners with perfect pitch. As I understand it, it doesn't help at all because perfect pitch is not precise enough to tell 440 Hz from 440.1 Hz for example, while you can do that easily with a tuning fork (once you learn how to listen for the beats). On the flipside, unequal temperaments - which are frequently used if you are a harpsichord tuner - are hell for people with perfect pitch who listen to only equally-tempered music. When you "merely" have relative pitch, unequal temperaments can actually be nice.

My mom says it’s helpful for her as a music teacher. It was annoying when she tried to teach me piano and she’d be cooking in the kitchen and I’d be playing in the other room and she’d call out when I made a mistake. But that’s probably just because I was an ornery student. Objectively my mom is a fantastic teacher. Her students all do really well in competitions and my nieces love playing with her. I’m sure perfect pitch is only a small part of it but it helps.

It seems like hearing someone make a mistake, especially on a piano (vs a trombone or violin), isn't related at all to perfect pitch... unless the mistake is playing the whole piece in the wrong key

That’s fair. I could also play any note on the piano and she would play the exact same note back.

As an amateur who does have it, yes, it's super awesome for transcription. However, I don't think it's very useful for anything else.