PostgreSQL – Pros and Cons of Checking Unique Column Value Before Insert

PostgreSQL doesn't have INSERT ... IGNORE so that isn't an option. You can use upsert-like operations (search for "postgresql upsert) but they certainly have a performance cost. Inserting and ignoring the resulting error on duplicate key is possible, but it tends to result in pretty spammy logs.

Personally, I'd do what's effectively do a bulk upsert, where I'd do something like this:

• CREATE TEMPORARY TABLE staging_table(...)
• COPY TO staging_table(...) FROM ... (or do bulk inserts)
• LOCK TABLE real_table IN EXCLUSIVE MODE
• INSERT INTO real_table(...) SELECT col1,col2,col3,... FROM staging_table WHERE NOT EXISTS (SELECT 1 FROM real_table WHERE real_table.primarykey = staging_table.primarykey)
• COMMIT

You can do an UPDATE before the INSERT if you want, updating existing records with new values.

The LOCK TABLE is necessary to prevent concurrent updates failing with errors. You can still SELECT from the table during the update.

If you EXPLAIN the plan for your INSERT you should see that it's been transformed into a JOIN when you're inserting larger numbers of records.

In Postgres, there are two ways to circumvent the chicken-and-egg problem of inserting into tables with circular references.

a) Defer one of the constraints, either declaring it as DEFERRABLE INITIALLY DEFERRED when created or as DEFERRABLE as created and then defer it when needed.

For an example of using deferrable constraints, see my answer in this question:
Implementation of a many-to-many relationship with total participation constraints in SQL.

b) Use a single statement to insert into the two (or more) tables, using modifying CTEs. Example for your case:

with
  insert_emp as
  ( insert into employee 
        (Fname, Minit, Lname, Ssn, Bdate, Address, Sex, Salary, Super_ssn, Dno)
    values
        ('James', 'E', 'Borg', '888665555', '1937-11-10', 'asda', 'M', 55000, NULL, 1)
    returning 
        *
  ), 
  insert_dep
  ( insert into sp0090.department 
        (Dname, Dnumber, Mgr_ssn, Mgr_start_date) 
    values 
        ('Headquarter', 1, '888665555', '1981-06-19')
    returning 
        *
  ) 
select *
from insert_emp as e
  full join insert_dep as d
  on  e.dno = d.dnumber
  and e.ssn = d.mgr_ssn ;