I tried to search for it in the official docs but no luck. Can Postgres 13 stored procedures return multiple result sets similar to SQL Server?
If you mean to return a result set by executing a plain query - no, such syntax is not supported in PL/pgSQL.
If you mean to return a result set by using a cursor - yes, PostgreSQL stored procedures can return cursors too.
You can define multiple cursor output parameters: https://www.postgresql.org/docs/13/plpgsql-cursors.html