Kernel 5.13 is EOL so please install both 5.4 and 5.10 LTS (Long Term Support) and see which one of the two troubles you least.
Fantastic! So what does:
echo 100 | sudo tee --append /sys/class/leds/chromeos::kbd_backlight/brightness
do?
Keyboard lights on now?
Unrelated to your problem, but you have both PulseAudio and PipeWire running and they could conflict. If you want a stable experience, do a:
systemctl --user disable --now pipewire.socket
systemctl --user disable --now pipewire.service
systemctl --user mask pipewire.socket
and if you like bleeding edge (unstable) do the opposite and disable&mask PulseAudio. 