SteamOS 3 is not as glorious as I expected but if you want to see it, here is how:

Preparation:
Download SteamOS 3 from here: link
It contains a single image file. Extract it. And backup the extracted image just in case, it keeps your changes and it seems to break very easily. Even clicking the "Steam" shortcut causes an "out of space" error at /home and breaks the image.
Install QEMU and edk2-ovmf. edk2-ovmf is UEFI firmware and SteamOS 3 boots only in UEFI.
Create an image file. I use
 
qemu-img create -f qcow2 /path/to/image.qcow2 64G
so I have a small image file that can grow up to 64 GB. With SteamOS 3 installed, my image file is currently at 15.7 GiB. Image creation might require root privileges. You may need to chown the image. Or probably I am doing something wrong regarding permissions

Boot & Install:
1. Boot up the image.
 
qemu-system-x86_64 -drive file=~/Downloads/steamdeck-recovery-1.img,format=raw,if=virtio -accel kvm -m 8G -bios /usr/share/ovmf/x64/OVMF.fd -smp cores=6,threads=2 -drive file=/path/to/image.qcow2,format=qcow2,if=virtio
* Using -cdrom won't work. I use -drive instead of -cdrom. if=virtio should speed up disk I/O operations a bit.
* -accel kvm enables HW acceleration for the VM. If it does not work, you may need to enable it in your firmware interface. Do not try to launch VM without KVM.
* -m 8G specifies the memory amount. 2G and above should work.
* -bios should point to edk2-ovmf firmware. This is the path on Arch (and derivates), change if necessary.
* -smp cores=x,threads=y defines number of cores and threads per core.
* the second -drive points to the qcow2 image you created.
* DO NOT USE SUDO.

The screen will go black for a while, you should eventually reach Plasma.

2. Set keyboard layout if neceaasry
You can do this from System Settings. Go to Input Devices > Keyboard > Layouts and click Add. Remove the default layout.i Apply changes.

3. Modify reimaging script
 
sudo fdisk -l
should show you a list of disks. Remember the device file of your disk. Open file ~/tools/repair_device.sh and change DISK and DISK_SUFFIX accordingly. They are near the beginning of the file. In my case I was
installing to /dev/vdb so DISK is /dev/vdb for me and DISK_SUFFIX is blank.

4. Install SteamOS

 
sh ~/tools/repair_reimage.sh
and wait as SteamOS dd's its partitions to your image file. Choose to stay in Recovery environment.

5. Chroot and modify

Replace /path/to/disk with the disk you installed SteamOS to.
sudo mount /path/to/disk4 (the 4 is not a typo) /mnt
sudo btrfs property set / ro false
sudo umount /mnt
sudo mount /path/to/disk5 /mnt
sudo btrfs property set / ro false
sudo umount /mnt
sudo steamos-chroot --disk /path/to/disk --partset A -- /bin/bash
sudo mount -o remount,rw /path/to/disk4 (the 4 is not a typo) /
sudo steamos-session-select plasma-persistent
* edit /etc/default/grub as noted below *
sudo update-grub
exit
sudo steamos-chroot --disk /path/to/disk --partset B -- /bin/bash
sudo mount -o remount,rw /path/to/disk5 /
sudo steamos-session-select plasma-persistent
* edit /etc/default/grub as noted below *
sudo update-grub
exit
The steamos-session-select command will make SteamOS start Plasma instead of gamescope. Replace with plasma-wayland-persistent if you wish.

Open /etc/default/grub (in both A and B) and remove the option fbcon:rotate=1 in GRUB_CMDLINELINUX_DEFAULT. Or... your ttys and splash screen will be rotated.

6. Restart
Power off the VM, remove  
-drive file=~/Downloads/steamdeck-recovery-1.img,format=raw,if=virtio
and restart the VM. You will see a black screen (again). Let it boot. The installed OS is terribly slow, I hope this is because I have my image file on my HDD.
I do not have a discrete AMD GPU and I don't want to mess up with the OS bare metal so no gamescope for me.

Feel free to write up your experiences.