Part of my problem is not knowing the names of what I'm referring to, so feel free to suggest title edits please.
A bathroom sink is draining very slowly after someone bearded shaved, despite them gathering most of the hair out of the sink. I expected some hair to be clogging the J-trap, but when I went to clean that out, I found there is no J-trap and instead the sink drains into the lower end of a cylinder, with the cylinders outflow on the top. Pictures below. It looks like a garbage disposal to me, but that doesn't make sense because this cylinder is not directly connected under the sink and also it is not powered.
I think the cylinder might have the same purpose as a J-trap, given water enters it low and has to rise up high to drain out. That would mean there is (always?) standing water in the sink's drain pipe, at the same height as the cylinder's outflow pipe, because how else would water leave this cylinder.
My question is: what is this cylinder, and how to I clean it out like a P or J trap? I thought to unscrew the base of it since it has the square bottom to grip and turn, then catch what drains out and use a stick to poke out remaining gunk. Figured I'd ask here first, and may also try plunging or poking around the sink drain itself first to see if that solves the problem. Thanks.