It is my code. I told the machine what to do and I paid for the license.
When a customer orders code at my agency and I write it myself and deliver it, this very code also becomes the code of the customer. That is because it was ordered and paid for.
This is how it works.
You're just another consumer, as you rightly point out, and you don't have the right to intrude on projects and communities that are not interested in AI slop rebadged under your name.