

Switchdesk is a GUI for changing the default desktop once they’re installed, not for installing desktops.
The top of the page you link explains how to install alternative desktops which is using DNF. The GUI route to do this would be to use a DNF frontend like DNFDragora and search for the relevant desktop metapackage, and then install that.



Before you do anything, backup /home.
You can reinstall your system while preserving and expanding your /home partition; this is probably the cleanest and safest way to sort your disk. It allows you to move the boot and filesystem partitions to the start of the disk while keeping /home untouched, and then separately resize /home to fill the rest of the drive. You could not reinstall and manually move the partition but it’s slow and riskier when messing with a boot and main filesystem partition; much easier to start again tbh.
I’d get a USB and install Ventoy on it. Ventoy is a great bootable USB tool that lets you drop multiple different bootable ISOs on it (instead of reflashing the drive every time) & pick one at boot; great for installs and also to keep around as a recovery drive. I’d then put on it an ISO file of your preferred linux distro, and also a separate ISO file of a good live distro for recovery. GParted Live is particularly good USB live distro for this because resizing the partition is the aim, but almost any good USB Live Distro will do
I’d then boot up the USB drive and select the ISO for your Linux distro’s installer. During install, in the partition section, I’d then use the partition tool in your installer. Dlete all the windows partitions (sda1, sda2, sda3 and sda4), and then delete the exisiting boot (/boot/efi) and root file system (/) and create new ones at the beginning of the disk: 1gb /boot/efi and 85gb / system partiton as you have now, and ensure the existing /home partition is kept and mounted as /home in the new install. You’ll have loads of free unpartitioned space; leave that for now.
After the system is reinstalled, I’d boot in, check everything is ok, and then restart and boot the USB again, this time selecting GParted Live. Then with GParted Live, I’d resize the /home partition to fill all the empty space.
But as I said, before you do anything, backup /home. Also before you do anything you can use a partition tool now (like KDE Partition or Gparted) to add a label/name to your /home drive so there is no confusion when you use use the Linux installer or Gparted later. But it should be clear from the size alone.