The air conditioning (A/C) is not working?

I have an automatic Golf FSI 2005. I'm not sure if it has a 1.6L or 2.0L engine, but since it’s not turbocharged, I assume it has a 1.6L engine.

The air conditioning (A/C) is not working. I’m uncertain whether the compressor has a clutch because there is a control valve connected to the back of the compressor with two wires, and I don't see any other wiring connections. When I turn on the ignition switch, I measure around 5V on one of the wires. I can see the high-side pressure switch, but I cannot locate the low-side switch.

There was very little refrigerant gas in the system. I safely evacuated and recharged it with Hychill Minus 30 after confirming there were no leaks during the vacuum process. However, the compressor did not engage, and I observed 80 psi on both the high and low sides. Additionally, the refrigerant paused halfway while entering the system.

I would greatly appreciate your assistance in troubleshooting the issue. Additionally, please provide the wiring diagram for the A/C, as well as the locations of the relays and fuses.