UPDATE: in the end, the only way to make the sound out of my HDMI is to use the HDaudio legacy driver by adding the options snd-intel-dspcfg dsp_driver=1 in the /etc/modprobe.d/snd-intel.conf file. Then running sudo dracut --force and reboot.
However, with the HDaudio legacy driver, DMIC wouldn’t work which is the expected behavior.
Fedora 36 default setting is options snd-intel-dspcfg dsp_driver=2 (SST driver). No matter what you do, the HDMI audio will not work, ever.
SOF driver, options snd-intel-dspcfg dsp_driver=3, is not supported on my laptop—Coffee Lake CPU at all. You can see more regarding this situation here.
Basically, I have to pick my poison between option 1 or 2 