AC is not working, light and fans are on but the AC compressor does not engage.

What is your question?

Fans work fine as well as the heater. When I press my AC button, I normally hear the compressor engage. Recently I have not heard it turn on, even when inside the buttons all look/read fine. I thought it was low on refrigerant and once I connected the refrigerant can to the low pressure port, the gauge read that it was too high. Is my issue a bad compressor?

What makes this problem better or worse?

Nothing make is better nor worse.

How long has your 2015 Hyundai Genesis Coupe had this problem?

2 weeks.