First confirm a fault. Set the thermostat for cooling at a low enough temperature to ensure the unit energizes. Verify both indoor and outdoor unit is operating.
With an accurate thermometer, take a reading of the discharge temperature at the unit. Following that, take a reading of the room temperature at a representative location. Allow adequate time for both readings to stabilize to ensure accuracy.
Compare the two temperature readings. There should be a 18-20 temperature difference between the room temperature and the discharge temperature.
If the discharge temperature delta is much less than this, first check the obvious:
Dirty filter
Fouled coil
Clogged discharge grille
If that all checks, confirm that the outdoor unit compressor is running, not just the outdoor fan. You should be able to hear the compressor start up. The refrigerant lines should feel hot to the touch.
Beyond this, most equipment checks will require technical experience and/or specialized equipment.
The type of refrigerant chemistry makes no difference to the performance of the unit, providing that the unit was designed to use that particular type of refrigerant. The differences in the various refrigerants has more to do with system volume, evaporation temperature, lubrication, abrasion resistance, etc. as well as ODP (ozone depletion potential), and GWP (global warming performance). In a properly operating system, the type of refrigerant makes absolutely no difference to the end user.
As always, offered only as opinion