How can I prove that I have ownership over code I wrote myself, and that it isn’t copyrighted somewhere in the world?

As long as you had no access to that code and have some proof of that then that should be quite easy. I.e. you never worked for a company that claims copyright on something you wrote.

Developers also “generate” code and are also “trained” on code they written as freelancers or employees for others which is potentially copyrighted.

Then you need to do a proper clean-room rewrite with people who had provably no access to the original code.

They have a long way to go, it’s not just AWS, they also use Google Workspace and Github.