> I assume the VDB is a Progresql, because the VDB has pg_catalog schema, please refer the below image
No, the pg_catalog is for our odbc connectivity that uses the pg protocol and clients - which expect pg system tables to fetch metadata.
> Now my question is: Can you please explain why the User-Defined Functions are not available in the VDB pg_catalog schema?
You must first create add a postgresql source to the vdb. However not all source functions will be available. You can however right click on the source and manually add the definition of any source function that you need.