Hello tf43. Welcome to the forums. I used to be a design engineer for Toyota, then Hyundai-Kia. Part of my job at Hyundai-Kia was doing A/C audits and A/C research. Probably 90% or greater of A/C problems root cause was a refrigerant leak. And yours sounds the same.
There is a sensor on the low side line. If that sensor measures pressure below a certain threshold, the ECU will not engage the compressor. Again, 90% or greater reason the sensor would measure below a certain threshold is for a lack of refrigerant (from a leak).
In the grand scheme of things, the A/C system is not very complex. But it requires a few select tools and a thorough understanding of how it works in order to be proficient with repairing it. If you have an A/C repair shop, it would probably be the most effective route. However in the U.S., A/C repair is generally expensive.
View my fuel log 2020 Mirage ES 1.2 manual: 42.6 mpg (US) ... 18.1 km/L ... 5.5 L/100 km ... 51.2 mpg (Imp)