I got my card working with Fedora 36 with all the latest updates applied, i.e. kernel 5.18.5 and sof-firmware 2.1.1. I had to increase the volume and correct the balance to hear any sound. It is very soft in my case. You could also try if you can hear something with a headset.
My drivers were updated, but what fixed it for me was messing with the sound card settings for sof-essx8336 in alsamixer. I just got some music playing in the background and went through the list of settings and unmuted/turned up every one of them until I could hear the music.
The sound balance does seem a bit wonky right now but i’m sure I can improve it by messing with the settings.
Glad to hear, that did the trick for you . As far as I know, support for the sof-essx8336 is relatively new and still a work in progress. Hopefully future versions of the sof-firmware (2.2 and above) will improve the support, both for you and me.