What’s the relationship between gain (dB) and power (watts)?

That Bryston gain switch would be to match the volume of two disparate amps on the same preamp.

MC running a clinic here. Nice. 

A master clinic involves the recognition that in power amps variable gain is just variable negative feedback. See Roger Modjeski for an EE w ears and many successful designs the variable NFB RM-9 being a sonic master class. The cool thing about variable NFB w time and phase accurate speakers is that the intrepid listener ( given a decent recording ) can discern how NFB effects image depth....
carry on....
see also Burning Amp

Often just variable NFB but sometimes just R....

I find that speakers that has a low db rating benefits from a higher gain amp.
speakers that has a higher db rating benefits from a low gain amp.
wattage remains the same.
Also don’t forget your preamp gain.