How can I save my Bazzite setup before trying another distro?

If you're mainly curious about how another distro works, try it in a virtual machine first. VirtualBox is one option. Give the VM some disk space and install the distro into its virtual disk, leaving your Bazzite installation in place.

It's a convenient way to explore, though it won't be quite the same as running directly on your hardware.

For a way back after replacing the installation, make a full disk image with Clonezilla. Boot Clonezilla from a USB drive and save the image to a separate external drive with enough space.

A whole disk image is more useful for this than saving only the main Linux partition, since boot partitions may be needed too. Check that the image was created successfully and keep a separate copy of any files you can't afford to lose. Restoring the image will overwrite the target disk, so double-check which drive you select.

You could install the other distro alongside Bazzite instead of replacing it. That gives you a choice at boot, but you'll need free space or another drive, and you'll need to be careful not to format the existing partitions during installation.

I'd still back up your files first. Dual booting keeps both installs available, but it isn't a backup.

For a quick look at a distro's desktop, an online distro demo is another option. It's less of a commitment than installing anything, although it won't tell you much about how the distro behaves on your own hardware.