Default catalog and schema are provided by the client tool if they are set.. they have nothing to do with the actual query. So in that sense the fact that schema is empty is perfectly fine.

I would consider this to work as designed.

Yes i agree that schema can be empty.
But the issue is the if schema is empty, current code would throw unsetDefaultExceptionSupplier because default schema is empty.
Throwing error is not what we expect as SQL could be valid.

• case 1 -> QualifiedName.of(defaultCatalog.orElseThrow(this::unsetDefaultExceptionSupplier), defaultSchema.orElseThrow(this::unsetDefaultExceptionSupplier), tableParts.getFirst())
• https://github.com/trinodb/trino-gateway/blob/main/gateway-ha/src/main/java/io/trino/gateway/ha/router/TrinoQueryProperties.java#L389

I am thinking sth like this where we have a set that has list of temporary tables that is created when parsing to a tree.

This part of code is where it builds tree i assume?
https://github.com/trinodb/trino-gateway/blob/main/gateway-ha/src/main/java/io/trino/gateway/ha/router/TrinoQueryProperties.java#L202-L203

private QualifiedName qualifyName(QualifiedName table)
            throws RequestParsingException
{
    List<String> tableParts = table.getParts();
    return switch (tableParts.size()) {
        case 1 -> {
            String tableName = tableParts.getFirst();
            if (temporaryTables.contains(tableName)) {
                // For temporary tables, use only the table name
                yield QualifiedName.of(tableName);
            } else {
                // For non-temporary tables, use default catalog and schema if available
                yield QualifiedName.of(
                    defaultCatalog.orElseThrow(this::unsetDefaultExceptionSupplier),
                    defaultSchema.orElse(""), // Use empty string if default schema is not set
                    tableName
                );
            }
        }
        case 2 -> QualifiedName.of(defaultCatalog.orElseThrow(this::unsetDefaultExceptionSupplier), tableParts.getFirst(), tableParts.get(1));
        case 3 -> QualifiedName.of(tableParts.getFirst(), tableParts.get(1), tableParts.get(2));
        default -> throw new RequestParsingException("Unexpected table name: " + table.getParts());
    };
}

Have not look at your code but yes .. query parsing should work with

• empty default catalog and empty default schema
• values in both

If that is not the case, thats a bug and you should send a PR to fix that for sure.

I am not so certain if behavior is defined in Trino for

• default catalog but no schema
• default schema but no catalog

so we should find out. It might be related to the USE comment where you have to specify both.

Also note .. in the CLI you can either specify catalog and schema, or just catalog, but no just schema.