No.
Pages no longer provides the user option to show or hide filename extensions on its Save panel. There is no fix for this in the application now.
A Finder Get Info panel can hide the extension, but it sounds to me as though your filenames are too long to make much of a difference if the extension is hidden or not. The filename will be truncated in Finder Icon or List view, and even in the filename portion of a Get Info panel for really long filenames. Even if the character count of the filename is less than the 255 character maximum.
This distills into changing from using paragraphs to name files to much shorter filenames. If you need to visually document what the file does, use the Get Info panel and enter a comment instead.