### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
case 1:
				EditorScale::set_scale(0.75);
				break;
			case 2:
				EditorScale::set_scale(1.0);
				break;
			case 3:
				EditorScale::set_scale(1.25);
				break;
			case 4:
				EditorScale::set_scale(1.5);
				break;
			case 5:
				EditorScale::set_scale(1.75);
				break;
			case 6:
				EditorScale::set_scale(2.0);
				break;
			default:
				EditorScale::set_scale(EDITOR_GET("interface/editor/custom_display_scale"));
				break;
		}
	}
	
	Window *w = Object::cast_to<Window>(SceneTree::get_singleton()->get_root());
	if (w) {
		w->set_min_size(Size2(1024, 600) * EDSCALE);
	}
	EditorFileDialog::set_default_show_hidden_files(EDITOR_GET("filesystem/file_dialog/show_hidden_files"));
	EditorFileDialog::set_default_display_mode((EditorFileDialog::DisplayMode)EDITOR_GET("filesystem/file_dialog/display_mode").operator int());