The connector schema tab only supports searching by table name. We have connectors that have more than a thousand schemas. Each schema represents a customer.  The schemas have the same set of tables.  Searching by table is useless for us as it will be found in all the schemas.

Please add search by schema name.  Better yet, please add support to search at all levels:  Schema Name, Table Name, and Column Name.

See example screen capture below of our connector that has 1600+ schemas.