[Juppstein]

I run Kodi as my GUI instead of explorer and have used steam launcher for around 7 years. In my case since the installation of the new Steam UI, Steam Launcher starts Steam in the background and does not close Kodi (Leia - Steam launcher version 3.4.1).  I have even tried the force close option, and this also does not work.  Instead of closing Kodi, the Kodi screen just blinks, as if it quickly loses then regains focus.

Not sure which OS you are running with but I had the same issue since forever. What helped in that regard was to create a small script which kills Kodi and set it as the "Run before Steam" script.  Mine, running in Ubuntu, looks like this:

#!/bin/bash
kodi-send --action="Quit"

kodi-send is part of the kodi-eventclients-kodi-send package in ubuntu.