In Godot 4.0, there are going to be new debugging monitors, including debugging monitors for custom code/modules. Since these monitors can be set to track a small portion of the game, they may be faster and not cause as big of an FPS drop.
As for now though, it sounds like the issue is that the project is either using VSync (set to 60 FPS) or Godot is struggling to maintain 60 FPS, and so the additional cost of the debugger is enough to knock it down by 20 FPS. While I have not personally seen such a large drop in FPS, I have noticed that in my projects there is a generally a 5-10 FPS drop with the debugger monitors enabled. If you have VSync enabled, I would try disabling it and see if that affects the FPS drop any, as then it may run at a high enough frame rate that everything is smooth and you can debug (though your GPU may run hot, since VSync is not enabled).