The Faulty Air Conditioning is not blowing cold cold

The first thing to check is to ensure the system has enough refrigerant. It sounds like you did this, so I will assume you did the obvious and eliminated it early. Given the system works, the fuses and relays are probably fine, so we can skip that as well. If you want to check the fuses and relays, that's fine, but they're probably not blown given it has power. Use a DMM like this: https://www.lowes.com/pd/Klein-Tools-Dig...
Also, I would check the cabin filter for dirt and replace it before going deeper - sometimes this will help especially if the filter is original (or very close to it, and it's only been done once or twice prior) and it's cheap enough at $10-20.

NOTE: I would buy the 6,000 count version for $100 if you can swing the extra $35, but you have to decide on that.

While not a hard requirement, running an all-system scan tool on the car will give you a clue. A basic scanner will not suffice for Hyundai/Kia cars with A/C issues; you need one that can read the proprietary codes. Either buy one or take it to a shop and pay them to scan it and give you a report of the codes, including the actual code (Ex: B (Body) and C (Chassis) DTC codes). You will likely need to pay for this, but if you want to obtain codes cheaply, then this is the way to go. I own an XTOOL scanner, which can do this, but it's also not cheap - it can range from $250-$300. Unless you do the work yourself or have a German car like a Mercedes or Audi on your shortlist, buying this for a heavily depreciated Kia from the era where they were more infamous for oil consumption/Theta II motors blowing up the cost of the scanner is high relative to the value of the cars once they hit 100k miles :/.

The common suspects (without codes) on Hyundai/Kia platforms are the blower resistor (though this is more associated with A/C issues where the refrigerant is fine but nothing works), or bad blend doors. If you decide to try a blind fix, I would recommend trying the blower resistor if you want the "easy fix," but it's generally not an issue unless the resistance is low - this is where a good multimeter comes in handy, as you can check it against what it should be.

As an example as this is not an exact figure this is what you want to set the meter to when you check:

The meter I used to show (Fluke 115) is a premium midrange meter. You absolutely DO NOT NEED THIS - save your money. I have it because I got a good deal on it and use them enough to justify the high cost of Fluke.

If you can and the module isn't potted, it's probably a single resistor - maybe two - on a PCB. read the resistors directly from the PCB. If you can't do this because it's sealed, some trial and error is needed.

You can also try the blend doors first - but if you do, do them all, especially if you're unsure which one is faulty. Now if you know the left driver is bad and the rest are fine, you can replace that one, but be aware that it's a big enough job that I usually recommend doing them in pairs, such as this: Bad left driver > Do both on the driver side. Get ahead of it or you may be kicking yourself.

If neither of these fixes works, you may have a leak in the system or a bad compressor that has seized up. Put some dye like this in the A/C condenser, run the car for a bit, and see if you see any dye: https://www.amazon.com/Interdynamics-Cer...

NOTE: You will need a special light and glasses: https://www.amazon.com/REALHUNLEE-Condit...

This type of dye only shows under the right conditions (UV light+glasses with the right light blocking)

If there are no leaks, I would check the compressor for leaks and seizure issues.