If the sound is present all the time, it kinda means it's not AC at all. The bearings that are spinning while disengaged are not spinning when it's engaged.

Might be alternator bearings?? Doesn't that share the same belt? When the AC clutches in, there's more load on the belt, putting different loads on the alternator bearings.

Or maybe it's just the belt getting old & hard. You can take that belt off to see whether the noise is still there. You'll get a battery warning light, but you can run like that for a little while.

oops... wait, you said V-6. I don't know what shares belts with what. But you can still take off belts to narrow down the noise.