You can't make an open source HDMI 2.1 driver:
https://arstechnica.com/gadgets/2024/02/hdmi-forum-to-amd-no...
Based on a web search, the answer is at [0] by somebodyelse, as follows: "If you want half-way recent codecs or HDMI standards in a diy hardware project the licensing and chipset availability will kill it unfortunately. The same developer has dropped the HDMI from the follow up project because as a DIYer you can't get the chips needed..."
Also, many people presumably do use a PC as a media server. But, I imagine one would still output that to "real" audio and/or video equipment, if one has a listening/viewing setup that warrants it.
Also, I think there are plenty of open source audio amplifier projects. That simpler problem is not exactly applicable to the OP, though, and not subject to the same licensing and chip availability issues as a full blown AV receiver, apparently.
[0] https://www.audiosciencereview.com/forum/index.php?threads/o...
Arent the numerous Android based media players just that?
I've wondered this too, and I even tried to build one a few years back, but I came to the conclusion that most people who care that much about audio don't really care about open source or hacking hardware. They like buying a big, expensive black box that just does the thing and are fine upgrading every few years. Everyone else buys sound bars and there's not much in between.