Headless Kodi in docker container → Audio output device - no device found


I’m in need for some help with a special headless Kodi setup.

My final goal is to run multiple headless Kodi docker containers on a Raspberry Pi (https://hub.docker.com/r/linuxserver/kodi-headless).
This multiple Kodi instances will work as multiple audio renderers which will serve as multiple audio sources to connect to an existing multiroom audio system.
For the audio outputs, I want to connect multiple USB audio cards to the USB ports of the Raspberry Pi (and maybe also use the onboard audio output).

After some quick testing, it seems that this is possible to setup but I have one problem that I can’t solve.
When I navigate to the Kodi audio settings to select an audio device there is the following: Audio output device → Error - no devices found.
I added the following to my docker compose.yaml file with the intention to share the audio devices with the container:

  - /dev/snd

Most likely this is not the right way to do this or not enough to give the result I want.
Can someone point me in the right direction? How can I get my audio devices visible in the audio settings of my Kodi docker instance?

Thanks in advance!