It appears that there is no documented function for scheduled execution in user-managed notebooks and you are correct in availability of this function in managed notebooks.
In the Google Cloud console, go to the Managed notebooks page.
Next to the managed notebooks instance that you want to use, click Open JupyterLab.
Your managed notebooks instance opens JupyterLab.
In the folder File Browser, double-click the example notebook file to open it.
Click the Executor button.
In the Submit notebooks to Executor dialog, enter a name for your bucket in the Cloud Storage bucket field, and then click Create and
select. The executor stores your notebook output in the Cloud Storage
bucket.
In the Type field, select Schedule-based recurring executions.
By default, the executor runs your notebook file every hour at the 00 minute of the hour.
Click Submit.
Your notebook file runs automatically on the schedule that you set.
This answer is the possibly the closest workaround I have encountered when running scheduled executions and this answer referenced using Google's Cloud Composer, GCP's take on cloud orchestration.