Can I GRANT SELECT on all schemas in a database?
You can wait for PostgsqlSQL v14 and its pg_read_all_data system role.
Other than that, you will have to grant USAGE on all schemas and SELECT on all tables individually.
GRANT SELECT ON ALL TABLES IN SCHEMA will make that job much easier.
My recommendation is to issue all these grants not to the end user role, but to an intermediate role that you then grant to the end user. That way it will be easy to drop qaread.