System:

Debian 13 KDE (actually MX Linux, but doesn't seem to matter)  
Wayland (xwayland installed as well)  
Docker 29.5.2

Dockerfile:

FROM debian:trixie

ENV DEBIAN_FRONTEND=noninteractive
ENV LANG=en_US.UTF-8
ENV LANGUAGE=en_US:en
ENV LC_ALL=en_US.UTF-8

# Set locale
RUN apt-get update && apt-get install -y --no-install-recommends \
        locales && \
    apt-get clean && \
    sed -i '/en_US.UTF-8/s/^# //g' /etc/locale.gen && \
    locale-gen

# Install Wayland-specific packages
RUN apt-get update && apt-get install -y --no-install-recommends \
        dbus \
        libwayland-client0 \
        libwayland-egl1 && \
    apt-get clean

# Install X-specific packages
RUN apt-get update && apt-get install -y --no-install-recommends \
        dbus-x11 && \
    apt-get clean

# Add contrib, default is only main
RUN sed -i 's/^Components:.*/Components: main contrib/g' /etc/apt/sources.list.d/debian.sources

# Add 32-bit arch for Steam libraries
RUN dpkg --add-architecture i386

# Install Steam
RUN apt-get update && apt-get install -y --no-install-recommends \
        steam-installer \
        pciutils && \
    apt-get clean

# Additional
# TODO: What is really needed?
RUN apt-get update && apt-get install -y --no-install-recommends \
        vulkan-tools \
        mesa-utils \
        x11-xserver-utils \
        libvulkan1 \
        mesa-vulkan-drivers && \
    apt-get clean

# TODO: Does `-storebeta` even work?
# https://developer.valvesoftware.com/wiki/Command_line_options_(Steam)
CMD ["/usr/games/steam", "-storebeta"]

To run the container:

xhost +
sudo docker run -it --name steam \
    -e XDG_RUNTIME_DIR=$XDG_RUNTIME_DIR \
    -e WAYLAND_DISPLAY=$WAYLAND_DISPLAY \
    -v $XDG_RUNTIME_DIR/$WAYLAND_DISPLAY:$XDG_RUNTIME_DIR/$WAYLAND_DISPLAY \
    -e DISPLAY=$DISPLAY \
    -v /tmp/.X11-unix:/tmp/.X11-unix \
    --privileged steam:trixie

(The --privileged part is only temporary until I found out which capabilities are actually needed. Please don't run your containers with --privileged.)

I get the GUI dialogs to download Steam just fine, so at least some display forwarding is working:

The installation works fine, but when starting Steam it seems like it's not able to find Vulkan devices and then doesn't open any Steam window. (The container is not stopping and I'm seeing repeated ./steamwebhelper output after this.)

[...]
Running query: 1 - GpuTopology
CVulkanTopology: failed create vulkan instance: -9
CVulkanTopology: failed to create vulkan instanceFailed to query vulkan gpu topology

Failed to query vulkan gpu topology
Response: 
Exit code: -2
[...]
Vulkan missing requested extension 'VK_KHR_surface'.
Vulkan missing requested extension 'VK_KHR_xlib_surface'.
BInit - Unable to initialize Vulkan!
[...]

However, Vulkan is clearly working fine in the container, as this commands displays the cube rendering just fine:

$ sudo docker exec -it steam vkcube
Selected WSI platform: xcb
Selected GPU 0: AMD Radeon RX 550 / 550 Series (RADV POLARIS12), type: DiscreteGpu

(I've also tried it on another (pure) Debian machine with a 2080Ti, but I've got the same issue.)

I've created other GUI containers in the past (Firefox for example) and didn't have these problems.

Does anybody have an idea and can point me in the right direction?