Solution
The create test results methods does not include the product field, as it is a separate entity. You need to first create a new product that can be linked to the part number of your choice.
In the Swagger UI look for the products methods and use the
/products Creates new products POST method:

In the body of the request, you can enter the part number that will be linked to that product name, in the above example the part number is 12345. Once that is done, if you create a new test result and set that the part number to 12345:

The part number will be assigned the product as configured in the previous steps, you can confirm this by querying the in the
Test Insights>>Results section of the SystemLink Server Web UI: