There could be another issue with the AC other than the compressor, as there is a safety built in to protect the compressor so that it does not contaminate the system with metal shards. If pressure is too high or too low, the compressor relay will not engage. There could be a malfunctioning expansion valve or a clogged filter drier, no way of knowing for sure without having a technician do a performance check.
The higher dollar shops will have a machine that can put a vacuum on the system to withdraw, contain, and measure how much refrigerant was present; it can also recharge the system with refrigerant and PAG oil as required then monitor high and low side pressures, which can determine component performance such as a clogged evaporator or leaking condenser. If the prospective repair shop does not have this kind of equipment and just relies on gauges, move on to the ones that do.
The 4th gen AC is very robust, especially compared to the Neon's, as they can handle the TX heat that pervades for 8 months of the year, and the defroster works well year-round. I found out the hard way that if ya do no have the AC or defroster running almost year-round, then that PAG oil will not lubricate the system seals and they will dry out and fail...it's cheaper to keep the AC or defroster on almost all of the time and dial in the temperature ya want, it's waaay cheaper that way.
Warranty will depend on the shop...I've had AC work done at Firestone as they have the right equipment and a nationwide network that can support any repairs required during travel...not cheap, but I have worked out deals with several locations to pull a vacuum on the system to withdraw refrigerant, let me replace the faulty components, then they charge my system with credit for the refrigerant they previously recorded. The AC tech doesn't get his hands dirty turning wrenches nor works on a scalding hot machine, and I save $$$ by doing the work and also not working on a scalding hot machine...everybody wins ❄️