A simple way to do it would be to rename all of your Btrfs subvolumes, then install the new system into different subvolumes (leaving the old installation intact) using this method: Multiple installations on one partition | Garuda Linux wiki
After the new installation is up, you can copy or move the @home subvolume from the old installation to the new, and delete any unneeded subvolumes to free up space.
This exact solution is described in another (old) topic here: