New Page/New Post UI not showing saved templates

It seems that changes are being rolled out to SharePoint Online tenants to how the new page UI works and it's been causing issues. 

On a site that had some page templates prior to this change being implemented, if I go to create a new News Post, I see options for "From Microsoft" and "Saved on this site". There are some new "made for email" templates on the "From Microsoft" tab and the "Saved on this site" tab shows all the page templates for the site - regardless of whether they were made from a news post or a page starting point. 

However, if I choose to create a new Page, I see the standard out of the box templates and a new Apps tab, but I cannot see the page templates on the site. This is the exact same page as the previous screenshot, but the page templates saved on the site only show up for news posts, not for pages. 

Even worse, if I go to a different site on the tenant that did not have any page templates saved to it prior to this change, I cannot get the "Saved on this site" option to show up for either news or posts. I created two new page templates on this site - one starting from New Post, the other starting from New Page, and neither of them show up when I try to create a new page or post. 

I created one of the page templates on Friday and it's still not showing up today (Monday). 

Does anyone know how to make the "Saved on this site" option show up when it's missing?