Like I said, I am not an expert on heating/cooling, I’ve just been involved in paying for and seeing to the installation of air conditioners/heatpumps etc many times. I’ve also had to make sure complaints about them “not working correctly” get handled.
What I can tell you is very simply, an AC takes warm room air, runs it through the AC, and blows back out air that has had heat removed from it. We don’t need to get more specific than that, but in both a wall unit and a central AC, the heat is dissipated to the outside.
Your living space is continuously heating up due to ambient temperature outside being hot.
A traditional central AC has a “return vent” or many return vents all through out the house, the system “sucks” air into those vents. It then has supply vents that blow out cold air. In a normally functioning system, the AC can take that air that is being “sucked in” and cool it by about 15 to 20 degrees. So that means you should be able to measure the temperature of the air (with an infrared thermometer) at a return vent, and then measure it at a supply vent, and find a 15 to 20F differential. You have an in-wall AC, I don’t personally know how to take this measurement on an in-wall AC–in my experience they are typically just replaced instead of being repaired, so I’ve never known people to do much diagnostics on them.
But what the sum of all this means: if the air going in is really really hot, the air coming out won’t be super cold. So yes, in extremely hot temperatures, your AC will “blow” warmer air, it should still (if it is functioning correctly) blow colder air than it is “sucking in.” But if you are used to be it being a more comfortable temperature, the perceived temperature of the air it is blowing will feel warm, and not particularly cooling.
For some quick envelope math, let’s say the air being sucked in is 100F. That’s a hot and unfortunate temperature. The air it can blow back out, at the very best, is going to be 80F. More likely around 85F. So an AC in those conditions set to 65F will run nonstop and will never cool to much below the mid-80sF.
Remember the whole residence is being heated up constantly from the outside. So even if it’s actually achieving say, 18F of cooling, unless your thermometer is right beside the blower, portions of the residence will be a lot warmer than that 18F differential. So in your bedroom it could very likely be 90-91F, in the kitchen maybe 88F, right by the unit in the living room, maybe closer to 85-86F.