As rncbc pointed out, it was a partial existence of PW in Ubuntu, if I read it correctly it's coming with any recent release somehow supporting browsers only. It was a long journey finding instructions online tailored to Ubuntu installing pipewire and set up to work with pulse, jack.
In first round I was stuck at a point built-in spearkers worked, headphone/line out not, but my bluetooth headset became working which was promising as it never appeared as an option at all. At this point, if I don't connect Zyn-fusion to anything, it still shows a working state via VU meters, but even this stopped working when I connected a USB device (let it be any of them). Also when I started Jack in this state I got a bunch of errors like Invalid container address 'engine':'sync':'(null)' supplied to method 'GetParameterValue'.. (org.jackaudio.Error.InvalidArgs) , and a single forum where someone got rid of it by deleting ~/.config/rncbc.org/QjackCtl.conf , and surprisingly this also made everything working, including the USB interfaces (however I don't understand what's happening under the hood).
As rncbc pointed out, it was a partial existence of PW in Ubuntu, if I read it correctly it's coming with any recent release somehow supporting browsers only. It was a long journey finding instructions online tailored to Ubuntu installing pipewire and set up to work with pulse, jack.
In first round I was stuck at a point built-in spearkers worked, headphone/line out not, but my bluetooth headset became working which was promising as it never appeared as an option at all. At this point, if I don't connect Zyn-fusion to anything, it still shows a working state via VU meters, but even this stopped working when I connected a USB device (let it be any of them). Also when I started Jack in this state I got a bunch of errors like Invalid container address 'engine':'sync':'(null)' supplied to method 'GetParameterValue'.. (org.jackaudio.Error.InvalidArgs) , and a single forum where someone got rid of it by deleting ~/.config/rncbc.org/QjackCtl.conf , and surprisingly this also made everything working, including the USB interfaces (however I don't understand what's happening under the hood).
So again, thank you very much for the help!