Databricks Unity Catalog allows fine-grained access control, which can be used to securely manage UDFs by controlling access at a very granular level. This means that UDFs can be secured based on user roles and groups, ensuring that only authorized users can access and execute them.

Other options like embedding UDF definitions in notebooks or relying on Databricks runtime to enforce access control are less secure and don’t offer the same level of control or scalability as Unity Catalog’s fine-grained access control. Using external databases and Databricks secrets to control access might also be useful, but Unity Catalog is the most direct and robust solution for managing permissions on UDFs within Databricks.