### 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
}
	singleton->editor_plugins_over->remove_plugin(p_editor);
	singleton->editor_plugins_force_over->remove_plugin(p_editor);
	singleton->editor_plugins_force_input_forwarding->remove_plugin(p_editor);
	singleton->remove_child(p_editor);
	singleton->editor_data.remove_editor_plugin(p_editor);
	for (KeyValue<ObjectID, HashSet<EditorPlugin *>> &kv : singleton->active_plugins) {
		kv.value.erase(p_editor);
	}
}
void EditorNode::add_extension_editor_plugin(const StringName &p_class_name) {
	ERR_FAIL_COND_MSG(!ClassDB::class_exists(p_class_name), vformat("No such editor plugin registered: %s", p_class_name));
	ERR_FAIL_COND_MSG(!ClassDB::is_parent_class(p_class_name, SNAME("EditorPlugin")), vformat("Class is not an editor plugin: %s", p_class_name));
	ERR_FAIL_COND_MSG(singleton->editor_data.has_extension_editor_plugin(p_class_name), vformat("Editor plugin already added for class: %s", p_class_name));
	EditorPlugin *plugin = Object::cast_to<EditorPlugin>(ClassDB::instantiate(p_class_name));
	singleton->editor_data.add_extension_editor_plugin(p_class_name, plugin);
	add_editor_plugin(plugin);
}
void EditorNode::remove_extension_editor_plugin(const StringName &p_class_name) {
	
	if (singleton->exiting) {
		return;
	}
	ERR_FAIL_COND_MSG(!singleton->editor_data.has_extension_editor_plugin(p_class_name), vformat("No editor plugin added for class: %s", p_class_name));
	EditorPlugin *plugin = singleton->editor_data.get_extension_editor_plugin(p_class_name);
	remove_editor_plugin(plugin);
	memdelete(plugin);
	singleton->editor_data.remove_extension_editor_plugin(p_class_name);
}
void EditorNode::_update_addon_config() {