### 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
return ERR_FILE_NOT_FOUND;
	}
	int prev = editor_data.get_edited_scene();
	int idx = editor_data.add_edited_scene(-1);
	if (!editor_data.get_edited_scene_root() && editor_data.get_edited_scene_count() == 2) {
		_remove_edited_scene();
	} else if (p_silent_change_tab) {
		_set_current_scene_nocheck(idx);
	} else {
		_set_current_scene(idx);
	}
	dependency_errors.clear();
	Error err;
	Ref<PackedScene> sdata = ResourceLoader::load(lpath, "", ResourceFormatLoader::CACHE_MODE_REPLACE, &err);
	if (!p_ignore_broken_deps && dependency_errors.has(lpath)) {
		current_menu_option = -1;
		Vector<String> errors;
		for (const String &E : dependency_errors[lpath]) {
			errors.push_back(E);
		}
		dependency_error->show(DependencyErrorDialog::MODE_SCENE, lpath, errors);
		opening_prev = false;
		if (prev != -1) {
			_set_current_scene(prev);
			editor_data.remove_scene(idx);
		}
		return ERR_FILE_MISSING_DEPENDENCIES;
	}
	if (!sdata.is_valid()) {
		_dialog_display_load_error(lpath, err);