Hard to say, but I can tell you that if your fans are not working properly that can result in much higher pressures for your A/C system, and the resulting added load on an aging compressor can kill it quite quickly.
Your Jetta has a plastic fuse holder assembly on top of the battery that is prone to melting. It’s a poor design and is unable to handle the current drawn by the electric fans.
If I remember correctly under certain conditions your fans are designed to run after engine shut-off to help cool things down. Fans running for 5 minutes will not kill a good battery. If it does, you need a new battery.
Your A/C compressor is part of a (needlessly, in my opinion) complex circuit that involves 2 pressure switches, the control panel, fuses and fusible links, the engine computer and the cooling fan control relay. Any one of these things could be at fault.
There are several independent shops in my area that specialize in VW/Audi or Euro cars. I’d find one in your area.