PostgreSQL Multiple primary keys for table are not allowed

Multiple primary keys for table are not allowed

The cause of error: There is already a primary key created.
Check the primary key or drop the existing primary key.

Create table and primary key

CREATE TABLE test.products(
  product_id numeric,
  product_name varchar(500),
  category varchar(100),
  price numeric 
  );
  
ALTER TABLE test.products 
ADD PRIMARY KEY (product_id);  

Messages

CREATE TABLE
ALTER TABLE

Error message example

ALTER TABLE test.products 
ADD PRIMARY KEY (product_id, product_name);  

Messages

ERROR: multiple primary keys for table “products” are not allowed