So likely the evaporator may be leaking. The cold part inside the dashboard. You may be able to verify by either noting flourescent in the evaporator water, at the condensate vent, or if you were to remove the blower in the passenger foot well, you may be able to insert the UV light and then use an inspection mirror to see the upwind side of the evaporator.

Did you verify that dye had preciously been in the system by observing it any where like in the service valve where you installed the refrigerant? Was it in the new refrigerant?
You could continue to "Gas n Go" until the hot weather breaks, but with the price of refrigerant these days, this may be not cost effective.

Here is a picture of a 2020 RAM getting reassembled after evaporator replacement. It is the labor involved that makes this an expensive repair.
Step one, evacuate the refrigerant from the system, step two remove the steering column, step three, remove the entire dash board and put it in the front seats...

It actually looks worse than it is but at least it is not a modern Camaro as step two is remove the windshield...



If you do it or hire a shop, I highly recommend using factory Mopar evaporator, heater core, and replacing a new Mopar ETS (evaporator temperature sensor).
You do not want to do this job twice...

 

Thank you, I will need to get another low pressure hose extension to add more dye. Previously purchased one doesn't seat correctly. Also, there isn't enough room for hose to operate properly if it did. I'll run UV dye and monitor as well as keep everyone posted if things change. Thank you again.

 

We have a syringe type dye injector that should fit in there. No refrigerant can, just a liquid dye that get measured (an ounce) into a syringe and pushed into the system.
Uhm, I may be talking out my 5 hole, I am unsure if the guys shoot that into a charged system or use it to introduce it before charging the system.
Perhaps they inject into the low pressure side when the system is running ( less than 40 psi)

Did you look into the service valve on the system with the UV light and glasses? Did you not see any fluorescent in the valve?

If not, perhaps this is the first time anybody has added anything and maybe your charge will last for another 15 years,,, If it aint broke, don't mess with it.

Let us know in a few months or a few years!