One USB C port stops charging on Monterey 12.5

I find the contacts inside the USB-C ports tend to become corroded from bits of liquid getting inside the port (they seem like magnets for liquid in my personal experience with our organization's Macs). These ports also tend to become oxidized as well which can make for a poor connection. Sometimes connecting & disconnecting a cable multiple times will clean the connector enough to allow it to work.

Each USB-C port also has its own dedicated chip on the Logic Board to control power & data.

AFAIK, the firmware has no bearing on the basic capability of powering or charging the laptop as that all must be controlled by the hardware circuitry. The firmware may perhaps have some minor impact on things, but firmware won't affect the basic charging/power process.

No, software has nothing to do with charging a laptop as it is all controlled by the hardware. If only one port is having issues, then you likely have a hardware issue with the laptop which will need to be repaired.