Ford Escape add coolant to my air conditioner

https://www.quirkparts.com/v-2008-ford-escape--hybrid--2-3l-l4-electric-gas/cooling-system--radiator-and-components

Videos as well

https://www.google.com/search?q=2005+Ford+Escape+XLT+V6+radiator+hose+diagram

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the larger line is from evaporator this is the low pressure port.
How to Add Refrigerant to 2005 2012 Ford Escape 2009 Ford Escape XLT 3 0L...

You have trapped air in the cooling system, open the bleeder(s) (if equipped) while filling OR raise the front of the car up as high as possible with a floor jack and fill the coolant recovery tank to the top and run the engine until it is hot but do not let it overheat, wait for the engine to cool down (the coolant will self feed into the engine) and add more to the coolant tank if needed

I have a 2012 Escape with the 4cyl engine.
The water (coolant) pump is located on the front of the engine.
This would be on the passenger side of the car. Towards the front, on the passenger side, the top pulley is an idler, the next one down is the water pump.
And yes, the lower radiator hose does attach to the engine right behind the water pump.
The 6cyl Escape may be different.

Low on refrigerant, Have system checked for leaks. If no leaks, they will charge system and if all is well, you'll be cool.
Links below could be helpful

Everything You Need to Know About Your Car Completely Firestone Firestone...

How to Recharge Your Car Air Conditioner

Follow the top radiator hose down to where it connects to the engine. You should find a dome shape item or a couple of smaller bolts that attach to the engine to the side of the radiator hose and the thermostat will be inside the housing. You will need to drain the radiator, remove the bolts holding the thermostat housing to the engine and remove the old stat and put in a new one be sure to make note of how the stat is facing when you remove it and put the new one in the same way. then reconnect the thermostat housing making sure the gasket is in place so it won't leak, then refill the radiator slowly so you don't cause an air lock in the radiator, with cap still off start the engine and allow it to warm up until the stat opens and then you will need to add more antifreeze to the system. Double check for any leaks. Turn on the heater and make sure you have good heat and you should be good

You add the refrigerant through the low side. On your car it will be the SMALLER diameter port.

Engine over heating can be caused by a number of things. When you say the water pump and radiator appear to be ok I am also guessing that you checked the coolant level to make sure it is normal.

If the level is low then you obviously have a leak. Insufficient coolant circulating will not cool the motor properly because it won't be able to draw enough heat out. If the level is normal then you need to check the thermostat to make sure it is opening properly. To do this, run the motor to temperature and check the top and bottom hoses. They should both be hot and firrm once the thermostat opens meaning the circulation loop is operating properly. If the top is hot and firm and the bottom is cold/soft or collapsed then the thermostat isn't opening.

If the thermostat is operating properly then you ned to look for some other obstruction or cause for coolant loss. Check the head/intake gaskets, hose connections, hoses, over flow tank, radiator fins, radiator side tanks etc..

Good luck.

You need to recharge the a/c through the low side with the engine running you should have around 25-30 psi on the low side and around 175-210 on the high side with the engine running at 1100 rpms.

This usually means add coolant.
With the engine cold, take the radiator cap off. Its probably low on coolant,fill it up and put the cap back on.Also check the overflow reservoir and if needed fill it to the cold line. You probably have a coolant leak that needs to be fixed.