Not REST api, but a work around I put together.
Try this:
To move a page as child page
curl -X GET \
'/pages/movepage.action?pageId=&spaceKey=&targetTitle=&position=append' \
-H 'authorization: Basic ' \
-H 'x-atlassian-token: no-check'
To move a page as top level page in space
curl -X GET \
'/pages/movepage.action?pageId=&spaceKey=&position=topLevel' \...