If an activity would normally consume credits it will still do so in the beta. For example, if you used ArcGIS Notebooks to geocode data, the geocoding would consume credits at the normal rate. If you use a notebook to do geoenrichment, the geoenrichment still consumes credits, and so on.
You are not charged any credits for storing notebooks for the duration of the beta.
If you have ideas on how credits should work with ArcGIS Notebooks after the beta, please share your feedback using the Comments section below.
It would be great if there could be an API call that would return the equivalent of the Show credits link in the Analysis pane in the Map tool. Maybe a switch on the geoprocessing tools that tell them to take the specified inputs and return the credit estimate instead of running. That way the code could protect against accidentally burning more credits than expected.