Is it possible to create a new page and have it listed in the layout and blocks manager drop down to be edited in the same way as Home page, checkout page, login page etc.
Go to Design > Pages. Create page then go to Layout tab and change anything. After save you will have a Custom layout specific to that page only
There is no option for Design > pages
Creating a page by using Design > Content works but it does not appear in the Layout option in order to modify it.
Open the page you create and go to Layout tab