Given there are no BDs (so they are theoretical) maybe there isn't a threshold defined?

A WD will slowly cool to a BD over Trillions of years, so it's all linear. Funnily enough, they are probably every shade of red/brown in-between - but "brown dwarves" are usually reserved for objects that never where "proper" hydrogen-fusing stars, but are large enough to fuse deuterium.

There's no hard threshold, the star just fades gradually from #FFF to #000.

A fully black dwarf would be so cold it would be indistinguishable from cosmic background radiation, but that's going to take at least a trillion times longer than the current age of the universe. Not just slightly longer.

Right. I'm just saying that if the are any black dwarfs (which there should not be), we should be able to find ~arbitrarily dim ones as well, down to our ability to see.