I found this topic: Mullvad Browser has released package repos for Debian and Fedora - #2 by Winter-in-America
And it contains the solution for the Mullvad browser:
On its current default settings, the mullvad-browser.desktop file contains on its Exec lines, the flag --detach, which causes the shell process that spawns the mullvad-browser to exit. This causes mullvad-browser to fail to stay open inside dispXXXX qubes, as the shell process exiting causes the dispXXXX qube to also shut itself down. So, you need to remove the --detach flag from the mullvad-browser.desktop file.
After removing the --detach flag and restarting the template, the disp VM remains running when I launch the browser.
Maybe this is the same problem for Chrome.