relay switch

I have used a thin piece of paper placed between the magnet plates to quiet noisy relays in the past.

Its likely its simply a coil whose plates are starting to vibrate, and it is VERY common with big power relays. If you've ever been in the main breaker room coming into a building or even distribution room, it is rare that some contactor, ATS, or transformer isnt singing the 60hz anthem. Not fun to listen to but i doubt you'll get it replaced unless its failing to stay closed.

Progressive Dynamics 5200 is their transfer switch.
Yes, it could be giving up the ghost or may just need connections tightened.
Odds are though tightening will or can only delay the replacement.
Disconnect from power source, remove cover to the transfer switch. Reconnect the power source and see if that is where the noise is coming from. Do not touch anything with your body.
Some transfer switches have parts available so you do not have to replace the box.