I'd put about 130 hours in into the special edition and wanted to derp around on a new character. So I hard saved my old one and went to start a new game. Played for a bit, got bored and went to reload my old character. She's not there.

I checked under the files and I can see all her previous saves but they don't show up in game and deleting the saves of the new from my files one doesn't remove that character's saves in game.

I specifically remember being able to see all the character's saves I ever created in the original game so how do I get my old character back in the new version?

Skyrim:SE like Fallout 4, parse character saves. As long as the character was created in Skyrim:SE, the save will include character name information to allow it to be parsed. From the main menu in Skyrim:SE. click load. This should list all characters. Click the character name then a save file. When you load a 'Character A' game save you cannot see 'Character B' save data until you go the main menu.