Menus: Remove floats from custom links section in the Nav Menus screen.

With the new admin design, there were some issues with floating elements in the custom links section of the classic Menu screen. This changeset simplifies the CSS implementation by removing floats and `wp-clearfix` classes from some elements in favor of a more robust implementation based on flex positionning.

Props audrasjb, huzaifaalmesbah, shailu25, nikunj8866, joedolson, khushi1501, ozgursar.
Fixes #64692.
See #64308.



git-svn-id: https://develop.svn.wordpress.org/trunk@62097 602fd350-edb4-49c9-b593-d223f7449a82