The iTerm2 hotkey window, is a floating window, which for example also works in a space with another Fullscreen window/app opened (without moving to another space.)
You could probably even use Hammerspoon to initiate the keyboard shortcut if you didn't want to mark the window manually.
It's described here: https://github.com/wez/wezterm/issues/1751#issuecomment-1973...
The iTerm2 hotkey window, is a floating window, which for example also works in a space with another Fullscreen window/app opened (without moving to another space.)