@AuspiciousSolitude - would it suit your needs to be able to drag Composer to its own screen?
I have put in a bug report about that currently not working properly here:
I think being able to have any chat, both Ctrl + L or Ctrl + I, on its own screen would help keep the Editor space ‘clutter free’.
I have found myself chatting with Chat GPT in my browser on another screen, just so I can keep the AI conversation and the code editor on separate screens.