This is a feature that I requested for the developer tools extension that was added but does not appear to be in the current SQL developer extension.
Many users, but data warehouse users specifically work in a large number of schemas and therefore having autocomplete for schema names is as much a big deal as having autocomplete for table names and columns.
When time allows could we please have auto complete for schema names added back to the new extension.
Bonus points if we can favourite schemas in the connection tree so we don't have to browse hundreds of schemas for the same group of ETL schemas that are used regularly.