I do this using Raycast, no matter which terminal emulator I'm using today (Terminal, Ghostty or Alacritty), I can just setup my global hotkey in Raycast and get the same "quake mode" everywhere.
Does the terminal appear instantly, and obscure everything else?
By default, the way MacOS does full-screen windows is by moving them to a space. Switching between the terminal and another application, e.g., Chrome, causes a large sliding animation between applications, which I absolutely do not want.
Oh I don't have it fullscreen, sorry, it usually covers the bottom half or bottom-left corner (depending on screen size). There it appears and disappears instantly.