Thanks a lot @ich777 for all your work!
Already reached out to @ich777 via PM, but adding this here to see if someone is experiencing the same issue:
I upgraded to 6.9.0-beta35 from the 6.8.3 nvidia kernel with hardware transcoding working in all containers (Plex, Jellyfin, etc.). After successful installation of the nvidia-plugin, the graphics card is showing up in settings and nvidia-smi, but I am unable to get hardware transcoding to work. As soon as I activate hardware transcoding in Plex, I get a black screen instead of the video. Software transcoding works fine.
Already tried uninstalling the plugin and reinstalling it, rebooted multiple times, removed and added the variables for the containers, to no effect.
Anyone else experiencing the same issue or any idea what could be the problem?
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EDIT: I have managed to get hardware transcoding to work in Jellyfin, but still no luck with Plex...
EDIT2: Switching docker-images from binhex/arch-plex to binhex/arch-plexpass did the trick. Hardware transcoding is working flawlessly now. Thanks @ich777!