When you reinstall KotOR, it does indeed keep your old savegames -- these do not get removed. KSE does not have any sort of internal memory regarding your old saves -- they really exist on your hard drive. The path to them can be found in your registry -- HKLM\Software\Lucasarts\KotOR2 in the Path string. That's how KSE found them.
If for some reason the path in the registry is wrong, you can manually change the path of where KSE seeks your KotOR installation by right clicking on the "Knights of the Old Republic" or "The Sith Lords" node in the treeview but you'll have to do this each time you launch KSE. (Usually just easier to change the path in the registry directly instead.)