I've been using the example to test this out...and a new page is indeed created. But it is not a child of the homepage - it sits outside that tree of pages as a brand new root page in the space.
How can I create a page under any particular page in a space?
In the comments there is mention of an "ancestors" attribute that can be used to set the parent page for the page you are creating. And that is part of the request body described in the API documentation.
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