He's got the same impaired executive function as hoarders do, even if he hasn't accumulated the sheer volume of stuff and trash hoarders do.
Some professionals call it "chronic disorganization"--some important (to him) objects may, in fact, be well-organized amid the chaos, but nothing else is, and he neither cleans up after himself (washing dishes and putting stuff away in the kitchen), nor takes any normal measures to prevent a mess from happening (such as using a fucking ashtray, and emptying it regularly). Something spills, and he might wipe it up--only to leave the dirty rag sitting there. Or he might not wipe it up at all, instead leaving it to stain whatever surface it's on.
He does not vacuum, does not dust, does not clean, period, and most of the time he's totally insensible to the filth. He just doesn't see it. If he does notice it, he probably tells himself he'll deal with it later, but never does. And, typical of people like this, he'll blame others for the filth he's created--nobody else will come scrub his apartment, so that's why it's a mess, not because he's made it that way, and keeps it that way.
It looks like he is taking trash out on at least a weekly basis, so he doesn't have massive piles of actual garbage, but any little stuff that falls to the floor just doesn't get picked up, nor do crumbs and bits of food in the kitchen (so of course roaches love his place).
He's got all those crappy plastic sets of drawers, but there's nothing in most of the drawers, and there's no order to the way they're arranged; they're just dumped here and there. That's common with this kind of disorder, too. Hoarders commonly have lots of plastic tubs that were originally meant to organize their mess, only to become part of it, and that's what's happening here with those plastic drawers.
People with this kind and level of disordered thinking are really, really hard to treat, even when they do want help; it's an ongoing struggle to stay fully aware of their environment and create new habits. And Tommy, as we know, never sees himself as the problem (which is why he's a cow).
He trashed his last apartment, he's trashing this one, and he'll trash the next one, and he'll only stop doing it when he dies.