I decided to give Qtile window manager a try. It's running together with GNOME. That is, at least the
gnome-session is running, launched from Qtile's autostart script.
However, the compose key, which I use a lot, does not work. I had it mapped under Caps Lock and it appears to be still there:
~:$ dconf read /org/gnome/desktop/input-sources/xkb-options ['compose:caps']
Still, the CapsLock acts as regular caps lock, not compose. What should I check? Do I need to start any additional GNOME component to handle it?