### 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
continue;
		}
		String path = res->get_path();
		if (path.begins_with("res:")) {
			int subres_pos = path.find("::");
			if (subres_pos == -1) {
				
				edited_resources.insert(path);
			} else {
				edited_resources.insert(path.substr(0, subres_pos));
			}
		}
		res->set_edited(false);
	}
	for (const String &E : edited_resources) {
		Ref<Resource> res = ResourceCache::get_ref(E);
		if (!res.is_valid()) {
			continue; 
		}
		Ref<PackedScene> ps = res;
		if (ps.is_valid()) {
			continue; 
		}
		ResourceSaver::save(res, res->get_path(), flg);
		saved++;
	}
	EditorUndoRedoManager::get_singleton()->set_history_as_saved(EditorUndoRedoManager::GLOBAL_HISTORY);
	return saved;
}
static void _reset_animation_mixers(Node *p_node, List<Pair<AnimationMixer *, Ref<AnimatedValuesBackup>>> *r_anim_backups) {