I think your issue is between Azure Synapse Analytics and the PostgreSQL database through the ODBC connection.
If you can connect and view tables outside of Synapse, then log in to the PostgreSQL database and verify permissions for the account being used:
SELECT * FROM information_schema.role_table_grants WHERE grantee = 'your_username';
Aslo, there might be an issue with the ODBC driver being used. Make sure you're using a compatible and updated version of the ODBC PostgreSQL Wire Protocol driver.
Please try and tell us :)