### 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 HELP_COMMUNITY: {
			OS::get_singleton()->shell_open("https:godotengine.org/community");
		} break;
		case HELP_ABOUT: {
			about->popup_centered(Size2(780, 500) * EDSCALE);
		} break;
		case HELP_SUPPORT_GODOT_DEVELOPMENT: {
			OS::get_singleton()->shell_open("https:godotengine.org/donate");
		} break;
		case SET_RENDERER_NAME_SAVE_AND_RESTART: {
			ProjectSettings::get_singleton()->set("rendering/renderer/rendering_method", renderer_request);
			ProjectSettings::get_singleton()->save();
			save_all_scenes();
			restart_editor();
		} break;
	}
}
String EditorNode::adjust_scene_name_casing(const String &root_name) {
	switch (GLOBAL_GET("editor/naming/scene_name_casing").operator int()) {
		case SCENE_NAME_CASING_AUTO:
			
			break;
		case SCENE_NAME_CASING_PASCAL_CASE:
			return root_name.to_pascal_case();
		case SCENE_NAME_CASING_SNAKE_CASE:
			return root_name.replace("-", "_").to_snake_case();
	}
	return root_name;
}
void EditorNode::_request_screenshot() {