### 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
bool all_saved = true;
	for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
		Node *scene = editor_data.get_edited_scene_root(i);
		if (scene) {
			if (!scene->get_scene_file_path().is_empty() && DirAccess::exists(scene->get_scene_file_path().get_base_dir())) {
				if (i != editor_data.get_edited_scene()) {
					_save_scene(scene->get_scene_file_path(), i);
				} else {
					_save_scene_with_preview(scene->get_scene_file_path());
				}
			} else if (!scene->get_scene_file_path().is_empty()) {
				all_saved = false;
			}
		}
	}
	if (!all_saved) {
		show_warning(TTR("Could not save one or more scenes!"), TTR("Save All Scenes"));
	}
	save_default_environment();
}
void EditorNode::_mark_unsaved_scenes() {