### 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
center_split->set_split_offset(old_split_ofs);
}
void EditorNode::_add_to_recent_scenes(const String &p_scene) {
	Array rc = EditorSettings::get_singleton()->get_project_metadata("recent_files", "scenes", Array());
	if (rc.has(p_scene)) {
		rc.erase(p_scene);
	}
	rc.push_front(p_scene);
	if (rc.size() > 10) {
		rc.resize(10);
	}
	EditorSettings::get_singleton()->set_project_metadata("recent_files", "scenes", rc);
	_update_recent_scenes();
}
void EditorNode::_open_recent_scene(int p_idx) {
	if (p_idx == recent_scenes->get_item_count() - 1) {
		EditorSettings::get_singleton()->set_project_metadata("recent_files", "scenes", Array());
		call_deferred(SNAME("_update_recent_scenes"));
	} else {
		Array rc = EditorSettings::get_singleton()->get_project_metadata("recent_files", "scenes", Array());
		ERR_FAIL_INDEX(p_idx, rc.size());
		if (load_scene(rc[p_idx]) != OK) {
			rc.remove_at(p_idx);
			EditorSettings::get_singleton()->set_project_metadata("recent_files", "scenes", rc);
			_update_recent_scenes();
		}
	}
}
void EditorNode::_update_recent_scenes() {