Can I run KDE and Gnome on bazzite?

Both GNOME and KDE Plasma are supported on Bazzite.

How can I install and manage multiple images?

Multiple images can only coexist as follows:

• Dual-boot
• Rebase to second image -> pin second image with sudo ostree admin pin <insert digit> -> rebase back to original image. From now on, you can access this second image from GRUB. It's recommended to designate a different user to the second image; and only access it through that. While what has been just described technically works, and you could even keep the second image up to date with a super cumbersome upgrade path, managing a system like this is not supported and could lead to unforeseen circumstances. Though, it is valid to pin your original image -> test another image through rebasing (and a new designated user) -> rollback to original image. Pinning the original image is not necessary, but I like to play safe. Note that rpm-ostree reset might be needed sometimes for rebasing.

Now I suspect that perhaps the game freeze wouldn’t happen with Gnome either. So I want to have both on bazzite, but can’t figure it out.

So, IIUC, you're just interested to know if this problem persists on GNOME or not. So, consider the following:

• Pin your current deployment with sudo ostree admin pin 0.
• Create a new user, but don't use it yet.
• Rebase to Bazzite's GNOME image.
• Reboot
• Enter through the new user (or create a new one).
• Test out whatever you want.
• Rollback through rpm-ostree rollback
• Reboot
• Continue using your original user.