Schedule C Payments Requiring a 1099

I'm confused where the Schedule C asks if I made any payments that would require me to send a 1099.  I found on the IRS site:  "If you paid someone who is not your employee, such as a subcontractor, attorney or accountant $600 or more for services provided during the year, a Form 1099-NEC needs to be completed, and a copy of 1099-NEC must be provided to the independent contractor by January 31 of the year following payment. You must also send a copy of this form to the IRS by January 31."

 

Reading the instructions for the 1099-NEC, it says merchandise is excluded in this, however what if I sell on-demand things like books that I have manufactured and sent to customers directly?  For example, I have used this site to send a book I made "on-demand":  https://www.publishingxpress.com/.  So, even though I am buying merchandise ultimately, they are providing the service of manufacturing the merchandise for me.  But, it would seem odd because everyone who uses that site would seemingly have to issue a 1099-NEC to that site if they paid $600 for their services?  Wouldn't the sites own payment handler send them a 1099 form if they make a certain amount?