Stick a thermometer in the vent. Should be around 50-60°F coming out. You’re potentially low on refrigerant. Any frost on the coil box (usually above the furnace)?

Unfortunately this is 100% not user fixable. Typically requires specialized tools to diagnose and then fix. You also can’t buy refrigerant without a license.

Another possibility is the starting capacitor for the compressor motor is bad.

If the capacitor is bad then the compressor motor won't actually start, but the fan will still turn on. This will make it seem like the AC unit is running, but there won't actually be any cooling going on. The fans will still blow air, and it'll feel slightly cooler because it's moving air, but it won't actually be cooler.

Replacing capacitors is pretty easy and not too expensive. However, it can be extremely dangerous so I recommend you leave it to the professionals unless you have some experience working with electricity.

Is the coil outside unusually hot or is the fan outside not running well? It should be moving a lot of air, not like a jet but not like a warm fart either. If that's the only problem then you're in luck.

You said there's cool air from the vents but less than you expect.. less cool or less air? If the blower motor isn't working right that's a fix you can do, you'd just need a new one of the same motor that is in there now. Then it's just a few bolts and screws, maybe a few wire nuts.

Is there icing up anywhere? Particularly at the coil inside the furnace. You may need to turn off the power and open an upper panel to get access to see. If that's happening then the other guy is right and you're low on refrigerant. A combustible gas tester is not super pricy but even if you find the leak you won't be able to fix it yourself.

Good luck.

100% low on coolant, which means you have a leak.

If it suddenly got really shitty, then it's a big leak and no way around it.

If it's slowly gotten shittier and shittier, so slow you're just now really worrying about it. Then it's likely a tiny pinhole leak. The environmently right thing to do is still to get the leak repaired, depending on your state laws you may not have a choice.

But for a pinhole you can charge it back up and could be good for years, could be good a week.

Now you're a renter, so if you're in a good state you maybe able to report the suspected leak, and then they have to get it checked?

It's one of those things where any one person has a negligible effect, but if everyone goes one way or the other it's a huge effect, so some states say you can't charge without doing a leak check and then they have to fix it before charging.

Cold but not blowing? Or blowing but not cold?

Some solid advice in here.

I'd also check the coils inside the unit. Look up under the filter you pulled. Coils are probably over that. Get a flashlight and have a look.

If they're coated in gunk, they make spray cleaners that dissolve the whole mess.

Not cold enough, or frozen solid, sounds like nasty coils to me.

Not sure how much a service call would be to an HVAC tech to come out and actually tell you what's wrong, but if you can afford to spring for it, at least you'll know, and have facts to go to your landlord with

You’ve checked everything that can be checked by you. Time to call a pro.

Check your breaker for the ac. If it's off the central blower will turn on but the ac unit (the part outside of the house won't turn on). Go outside and look if the fan out there is spinning.