How does PostgreSQL Foreign Data Wrapper (`postgres_fdw`) enable cross-database federated queries?

Configuring postgres_fdw

CREATE EXTENSION postgres_fdw;

CREATE SERVER billing_server
    FOREIGN DATA WRAPPER postgres_fdw
    OPTIONS (host '10.0.0.50', dbname 'billing_db', port '5432');

CREATE USER MAPPING FOR current_user
    SERVER billing_server
    OPTIONS (user 'db_reader', password 'secret');

IMPORT FOREIGN SCHEMA public FROM SERVER billing_server INTO foreign_billing;

-- Query local and remote tables seamlessly in a single SQL statement
SELECT c.name, b.invoice_total 
FROM customers c
JOIN foreign_billing.invoices b ON c.id = b.customer_id;