I wanted to say thank you for this thread and help that search engines rank that real solution higher. With my HP ProDesk 400 G5 (i3) I had the same "no sound via HDMI" issue, also in a parallel Kubuntu 22.04 install. Then it was clear that it is a general Linux issue and not restricted to LibreELEC. After learning about alsa's hdajackretask tool, I managed to get sound in Kubuntu by connecting the three pins that were shown as unconnected. I also selected "auto model" in hdajackretask which at least did not hurt. Hdajackretask then just added two files to the system to keep the settings persistent. After verifying that those files reliably enable HDMI audio output surviving reboots, I copied the files over to the LibreELEC install to the corresponding locations given in this thread. However, I had to create the "firmware" folder first to put the hdajackretask file in. After a reboot, it worked immediately, i.e. the output devices showed up in the config dialog.
Thank you for that information, that was quite a long search to get there! I could ignore all the other tips regarding cabling etc. as another parallel install of Windows 11 (yes, 3 OSes on the machine) showed that it works in priniciple and that it has to be a Linux issue.
Now I have to figure out where I would file that bug with the alsa people. Maybe it has to do with the Conexant CX20632 HDA sound chip in the HP device that is maybe not that common. Any hints where to submit that issue that the device quirks are added upstream?
Best regards
weaker