Thank you for reporting back! Much appreciated!

So it turns out, I cannot use my NVIDIA card using distrobox. I guess it only works with AMD?

Interesting. Unfortunately, I don’t own an Nvidia device. Therefore, I can’t tackle it myself. Distrobox should allow the use of Nvidia, but I’m unaware if this applies to the bazzite-arch container as well. The picture you shared and the link to its FAQ-page (found below) do suggest otherwise, unfortunately…

I was wondering if distrobox would somehow allow better performance

FWIW, I’ve always experienced better performance inside the bazzite-arch distrobox container, at least compared to Flatpak*.

I see that this image is used a lot on Steam Deck, which I also don’t understand why (as opposed to having everything native).

Because the distro image it’s used in conjunction with, Bazzite, is Fedora-based, while Steam OS is based on Arch. Bazzite is Fedora-based in the first place, because Arch doesn’t officially have any plans for ‘immutable’ distros yet. As for the remaining distros, only Fedora and NixOS (see Jovian-NixOS) have a sufficiently mature and suitable platform at this point in time.

maybe I am missing some graphical dependencies

This happens way more often than you might expect. Even the so-called ‘toolbox’ containers from Distrobox miss a lot of packages required to support software graphically. Consider running it inside a terminal and pay attention to error codes etc; those might/should help you resolve the issue. Sometimes it helps to explicitly use the -v or --verbose option to ensure that the program actually communicates what’s happening.