@Aaron_Wolf that likely has something to do with your configuration or your distro. I also have a Framework 13 AMD running Arch Linux with PipeWire and the configuration as described in the first post works for me.
I have to manually switch to the headset microphone via pavucontrol or some other PulseAudio/PipeWire configuration tool though. The headset microphone can be selected in the “Port” dropdown of the “Family 17h/19h HD Audio Controller Analog Stereo” device as “Headset Microphone”.
EDIT: I found a way to make it automatically switch by editing /usr/share/alsa-card-profile/mixer/paths/analog-input-headset-mic.conf to have a priority of 90 instead of 88, but there must be a better way to do that since that file is not a file that should be manually edited normally.