### 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
const EditorPlugin *self_owning = Object::cast_to<EditorPlugin>(context);
				if (self_owning && self_owning->can_auto_hide()) {
					context = nullptr;
				}
			}
			if (!context) {
				to_remove.push_back(kv.key);
				for (EditorPlugin *plugin : kv.value) {
					if (plugin->can_auto_hide()) {
						_plugin_over_edit(plugin, nullptr);
					} else {
						_plugin_over_self_own(plugin);
					}
				}
			}
		}
		for (const ObjectID &id : to_remove) {
			active_plugins.erase(id);
		}
	}
}
static bool overrides_external_editor(Object *p_object) {
	Script *script = Object::cast_to<Script>(p_object);
	if (!script) {
		return false;
	}
	return script->get_language()->overrides_external_editor();
}
void EditorNode::_edit_current(bool p_skip_foreign) {