Where is the blend door actuator located?

Which part are you referring to? There are two 5 wire actuators, the Mode door motor is on the left (drivers' side) and the air mix door motor is on the right side. You'll have to identify them by their wire coloring, the two actuators at the bottom of this wiring diagram. Both use the same purple power wire. They are both stepper motors as well.

The Air mix door book time for labor is 0.5hr so it can't be too difficult to get to.

So with all the doors set in the "A" position, Full Cold, the rear and front Foot (floor) vents should be closed. Both front side dash vents should be open, defrost should be closed, Recirculation Air should be On, and it sounds like youre not getting heat from the heater core or it would be very hot. So the warm air youre getting has to be from just outside air, the only way to verify the door positions would be with an enhanced scan tool to see the HVAC control module's live data, which should be able to show the positions of each door and bi-directionally control the doors.
Can you hear the Recirculation door move when pressing the button? They are usually noticeable when the doors are moving. I would get a full system scan done for codes in the HVAC module. You dont want to take half the dash apart and not be able to tell what doors are moving to the correct positions or not, especially with rear air vents as well. When Im dealing with these situations the first thing I go to is a good scan tool to see whats going.

You'll need a scan tool not just a code reader, code readers will only read codes from the engine computer, not read codes from other modules such as the HVAC or BCM. Along with live data from those modules, You could have a shop do a full system scan and just get the codes, not necessarily have them repair it. Just swapping out parts can get very expensive quick.

Okay, lets see what you come up with. I know some diags are a pain, believe me, Im fighting with some other vehicles right now that are just being extremely difficult, especially with emissions related things.

Ok you'll have to check it for power on the Purple wire with the key On, the other 4 wires are for the stepper motor windings, stepper motors work just like the name sounds, they move by a certain amount of steps to the position needed. Which makes them a little more difficult to diagnose than a regular DC motor. Ill post the wiring diagrams again, but you either have a bad actuator or the control unit is bad and not moving that one actuator.

This is the wiring diagram (top and bottom) for the Heater/AC controls. I assume you have identified the correct connector by the 5 wire colors? I would use a test light and multimeter to check for power on the Purple wire, since the test light will put a little bit of a load on the power wire, and then the multimeter will verify youre getting a full battery voltage to the actuator. Its odd youre getting warm air out of one side on this system, if its a manual system and the drivers side and passenger side cant be controlled separately. I would also check Fuse #5 10amp in the driver side dash fuse panel, make sure there is power on both legs of the fuse, You mentioned you already have a new actuator, did you install that yet?

https://www.2carpros.com/articles/replace-blend-door-motor

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

https://www.2carpros.com/articles/how-to-use-a-voltmeter

This is the procedure for checking the mode door, since its the same type of stepper motor that the air mix door is you can use this to check the motor for the air mix door. The first diagram mentions terminal 5, thats the Purple wire (pin 5) of the doors connector. And on diagram 5 you can unplug the connector and check the resistance of the motor itself, since all of the 4 windings should be the same resistance, measure from pin 5 to each of the other 4 and you should read about 90 Ohms for each one.

You didn't move the door manually with it still hooked up to the actuator, correct? You disconnected the rod first, because you can't force the actuators open by hand, they can be damaged that way. If the A/C is not as cold, the air mix door is not fully in the correct position. Are you sure you replaced the correct actuator, and not the Mode door actuator? The mode door actuator is what directs air flow to either the floor or dash vents etc. The Air mix door is responsible for the air temperature.
The rod for the door should be in the same position on the white piece as it was before the actuator was replaced.
The HVAC actuators may need to be recalibrated when one is replaced. This is usually done with a scan tool that has calibration options. This is also where having the HVAC module scanned for codes would have been a good idea, it would have directed you to the exact problem instead of just changing a part. You should see the air mix door move its full range when changing from full hot to full cold. It's possible there are other issues going on here. Did you change the actuator with the correct wire colors for the air mix door? This one here.

But you did have very cold air coming from one vent before replacing the actuator? Its possible there is a leak and its low on refrigerant, but the warm air from one vent and cold air from the other is a bit odd when this doesn't have an air mix door for each side, To determine which actuator you replaced, I would go by the wire colors on its connector, each 5 wire actuator has different wire colors. But at this point having the pressure and levels of refrigerant is a good idea, I would also ask them to check the Heater control module for any codes, and they can also look at live data from that module to make sure there are no temperature sensors reading incorrectly and also run a recalibration on all the doors. You can see by the operations below, the door positions depend on a few different temperature sensors and even engine rpm. So it can get a bit complicated with the newer systems, even though the car is already over 10 years old. At least they should be able to tell you if there are any other faults in the system.