Hopefully he survives it. I keep my fingers crossed.

Since you don't want a tiling wm, the cosmic desktop just entered alpha and is supposed to be fairly lightweight for a full DE.

https://wiki.archlinux.org/title/COSMIC

I use arch hyprland, btw.

If you're not into tiling, install openbox and a panel of your choosing. You will quickly find that you don't need a DE at all.

I like IceWM pretty well... for a non-tiling WM, that is. 😉

It's very lightweight.

while I'm not sure about the tiling WM front I can help with the KDE optimization on Arch part:

To preface I'm sharing sections of my Bash script that I'm in the process of eventually releasing under AGPL-3.0 which should help explain the editing/verboseness of them.

For base/minimal Arch Linux Packages:

## `btrfs-progs` is dependent/only required if you use BTRFS as your file system.
## `grub` is also dependent if you use GRUB instead of Systemd as your init system.
## intel-ucode replaces amd-ucode (as discerned from your comment on this post) which installs Intel-based microcode for your processor/CPU.
pacstrap -K /mnt intel-ucode base base-devel btrfs-progs efibootmgr grub iptables-nft linux linux-firmware linux-lts man nano networkmanager pipewire pipewire-alsa pipewire-jack pipewire-pulse sudo

For Installing Core Packages

### grub-btrfs is omitted as it is orphaned as of Sept 3, 2024. https://archlinux.org/packages/extra/any/grub-btrfs/.
pacman -S --needed bash-completion cryptsetup dnsmasq e2fsprogs efibootmgr firewalld man-db networkmanager sddm sddm-kcm

KDE Focused Packages

## Installing plasma Group Packages
## https://archlinux.org/groups/x86_64/plasma/
pacman -S --needed breeze breeze-gtk discover drkonqi kactivitymanagerd kde-cli-tools kde-gtk-config kdecoration kdeplasma-addons kgamma kglobalacceld kinfocenter kmenuedit kpipewire kscreen kscreenlocker ksystemstats kwallet-pam kwayland kwin kwrited layer-shell-qt libkscreen libksysguard libplasma milou plasma5support plasma-activities plasma-activities-stats plasma-desktop plasma-disks plasma-firewall plasma-integration plasma-nm plasma-systemmonitor plasma-thunderbolt plasma-vault plasma-workspace plasma-workspace-wallpapers polkit-kde-agent powerdevil qqc2-breeze-style systemsettings xdg-desktop-portal-kde

## Installing kde-applications Group Packages
## https://archlinux.org/groups/x86_64/kde-applications/
pacman -S --needed dolphin kate kmix konsole kwalletmanager

AMD GPU Related Packages

## Installing Video Drivers
## FOSS AMD GPU Drivers
## Please see the table on https://wiki.archlinux.org/title/Xorg
pacman -S --needed mesa vulkan-radeon libva-mesa-driver mesa-vdpau xf86-video-amdgpu

## Enable the multilib repository for 32-bit application support:
sed -i "/\[multilib\]/,/Include/"'s/^#//' /etc/pacman.conf

## To enable 32-bit application support, the multilib repository is enabled by default using the sed command above. This allows the necessary drivers to be installable from the multilib repository.
pacman -S --needed lib32-mesa lib32-libva-mesa-driver lib32-vulkan-radeon lib32-mesa-vdpau
## Owners of older AMD graphics cards (GCN 1&2) may also want to install the ATI driver:
#pacman -S --needed xf86-video-ati

Some packages were omitted from the installation lines above as this was taken from my custom installer for self-hosting services.
I'd recommend checking the links provided above to to figure out what additional packages you want for yourself🤗

If you still have issues with KDE X11/Wayland on Arch or Ubuntu, feel free to DM me and I'll try my best to help👍

Just on the KDE front, I'm assuming you've optimised your KDE set up for your PC?

If not, first open your Settings app and in the search box type "Effects" - disable all the fancy desktop effects.

Next, if you're on X11, go into the "Display and Monitor" section and disable compositing (you can also temporairly disable this with Alt+Shift+F12 to see what impact it has). This option is not available in Wayland; but you may be better using X11 if you don't have a dedicated GPU? I'm not sure I'd be messing with Wayland on an old laptop; I've had serious issues on a high end PC - definitely improved with 6.1, but I'm using X11 still.

But KDE 6 isn't as svelt as KDE 5 was, so even optimised it may just not be up to the job.

XFCE is a good shout, and should run nicely on a 2013 laptop.