Here’s my system:
CODA CSiB integrated amp - custom tuned
Custom tuned. When and by whom?
Within a few months of purchase
There's a clue. What else happened within a few months of purchase?
I noticed a buzzing noise coming from the speakers whenever the amp was powered on (bias “on”), but no noise in standby mode (bias off).
Possible clue. Does the amp mute output in standby?
Thinking that it might be a noisy circuit,
Yes and if the amp doesn't mute output then guess which one.
I've never been one to shotgun a problem throwing parts at it but if the amp doesn't mute the output and its quiet in standby without tube bias then the odds-on favorite is the bias circuit.
Coincidentally (?) the very circuit one would think likely needs to be modified or adjusted in an amp custom tuned to alter the power at which it switches class.