How to check role of current PostgreSQL user from Qt application?

The manual:

SELECT current_user;  -- user name of current execution context
SELECT session_user;  -- session user name

Meaning, session_user shows the role you connected with, and current_user shows the role you are currently operating with, for instance after calling SET role some_other_role;.

You can check PostgreSQL user permissions with this query:

SELECT * FROM pg_roles;