For anyone having the issue of not seeing pages in the parent page dropdown here in 2025. The dropdown on the new editor limits the list to 100 pages. So if you have more, you will not see the new pages. The way around the limit of 100 pages without adding a plugin is to go to the Pages overview page like you're going to edit a page. Click Quick Edit on the page you want to set a parent page to. And there is the old classic dropdown there that will list all your pages.