not really a solution but i highly recommend getting either just a dac or a dac + amp, doesn't have to be a super fancy one but it leads to way less issues with sound in my experience. if you go down this route make sure it's "driverless" or something similar advertised for mac i think, otherwise i recommend the fiio e10k
for actual advice, you can check that the right module is loaded, looking at 'lscpi -nnk' it seems like snd_hda_intel is the one used for most audio devices. i would look into it and see if there are some module options for maybe forcing the internal header to be registered if that turns out to be the issue. googling i find this thread https://ask.fedoraproject.org/t/headphone-audio-not-working-asus-rog-strix-z590-f-alc4080/19253/5 but i really cba reading through it but maybe you find some helpful advice
also highly recommend getting rid of pulseaudio and just using pipewire and pipewire-pulse, since you're on arch it's probably something like 'pacman -S pipewire pipewire-pulse wireplumber' then i think 'systemctl --user enable wireplumber' should be enough