For Chrome inside a container, I also install the Google Talk plug-in. Unsure if that's still required, but things work well.
[1]: i.e. "--group-add plugdev", "--device /dev/hidraw4", "--device /dev/video4", "--device /dev/snd", "--device /dev/sri" and similar
I used system containers in the past, they are not always easy. No idea whether it would work with podman.
Now that I think about it: The browser obviously uses the display of the host. How? Only over X11 network protocol? That worked in the past, does it still work today? I thought modern browsers would need /dev/dri/? If that is made available, why would Webcams not be possible?
If you read the examples you'll see that they mount /tmp/.X11-unix in the container, thats where the X-Sessions Unix domain socket is. You can do the same for pulseaudio. But you shouldn't. Use Wayland and Pipewire if you are actually interested in using this as a security measure, since they are built for sandboxing.
> I thought modern browsers would need /dev/dri/?
They only need it for hw-acceleration. You can also give the container access to it if you need that.