Opened Audition Project and all 62 files are offline. Link Media isn't helping.

As SteveG said if the media was where they were saved then the session would open and find the media.
The sesx will look first in the absolute path for each media file eg
<file absolutePath="W:\Server\Big Disk\E Drive\Suite Spot Studios\Hearts Sessions\It Wont Be long\It Wont Be long_Recorded\Kick Trig_001.wav"
and if the media file is not found it will then look in the relative path as defined for that particular media file which in the example is
relativePath="It Wont Be long_Recorded/Kick Trig_001.wav"/>
If you copy a session and think you are working on the copied files and not the originals you would be mistaken.

View your sesx with a text editor (make a copy of the sesx  in case you mess with it) and scroll to near the bottom and you will see you media listed and you will see where the sesx is expecting the media to be - if the media is NOT in that location then that would be the issue

The basic rule is that as long as the files are in a location referenced by the session file, the session should open correctly. I'd move all the files and the session file to the correct folder, and even if they don't immediately come up in the correct place, then they should be relinkable easily.

It's a pain when this happens, and it's largely due to Audition's behaviour about saving, which always assumes that you want to save something in the same place as last time you did a save - which frequently isn't the case! I'd prefer a system that at least gave you a choice - so either the last location or a new/different one, and just click on what's appropriate. I think that with a system like that, this sort of thing would happen less frequently...