### 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
SceneTreeDock::get_singleton()->instantiate(p_path);
}
void EditorNode::request_instantiate_scenes(const Vector<String> &p_files) {
	SceneTreeDock::get_singleton()->instantiate_scenes(p_files);
}
void EditorNode::_inherit_request(String p_file) {
	current_menu_option = FILE_NEW_INHERITED_SCENE;
	_dialog_action(p_file);
}
void EditorNode::_instantiate_request(const Vector<String> &p_files) {
	request_instantiate_scenes(p_files);
}
void EditorNode::_close_messages() {
	old_split_ofs = center_split->get_split_offset();
	center_split->set_split_offset(0);
}
void EditorNode::_show_messages() {