You can run different userland drivers but not kernel drivers. Thankfully the kernel drivers are pretty much unified for AMD. to use the proprietary ones, install the appropriate driver in the distrobox container.

Vulkan and Opengl are different drivers so you will need to figure out the flags you need to set appropriately. arch wiki is a food resource for this.

For rocm and stuff make sure your kernel has the necessary bits, this will be distro specific, but I can at least say arch will work fine simply. and fedors too iirc

The driver runs in the kernel, distrobox still uses the host kernel as it is container based so no, you can not run two different drivers on host and in distrobox. That wouldn't even work in a VM though unless you have a second GPU you pass through to the VM. How do you imagine one piece of hardware to be simultaneously controlled by two different drivers?