Battery won't make a noise like that.
Water pump is driven by the timing belt. It can have noisy bearings, but I'm guessing that isn't it.

It could be the other things, you have to check each to rule it out.

Old, hardened belts will get quiet with belt-dressing. Not permanently, but then you'll know which one it is. If it's the bearings for the idler or the AC clutch, then dressing won't make it quiet.

Take the belt off & spin each pulley. Listen & pay attention to how smoothly each one spins.