You need to make it a floating window so it can overlap fullscreen windows of other apps:
[![enter image description here][1]][1]

This is in Profiles → Keys → Configure Hotkey Window.

- [@gnachman][2]


  [1]: https://i.sstatic.net/OvxYq.jpg
  [2]: https://gitlab.com/gnachman/iterm2/-/issues/9621#note_559614115