Have you Registered the new ST4 Serial Number. If so, then you should see the ST4 sounds library downloads in the [Sounds} tab of the IK Product Manager.
In the [Software] tab it says "Update" for ST4 as there is a newer version than the one you have installed. The software for ST4 CS, ST4 SE and ST4 (and ST4 MAX) is all the same. The features and sounds available depend on the Serial Number.
I would do the Update to ST4 in the IKPM, then Unautorize it (!), Register your ST4 Serial Number and Authorize ST4.
If you still have the ST4 CS or ST4 SE sounds libraries on disk, then you can direct the IKPM to install all the new ST4 sounds into those same folders. Before you install any of them, click "... More options", select "Install to... " and navigate to your existing library (select the folder that contains the existing "Instruments" and "Samples" folders and other stuff).
For AmpliTube, AT5 SE is an edition with a particular set of gear models, and AT5 Upgrade gets you the full AT5 edition. There is a Comparison Chart PDF on this page:
https://www.ikmultimedia.com/products/amplitube5/index.php?p=versionsIf you bought AT5 SE (i.e. not a bonus etc) and you are not relying on it to be a Qualifying Product (for any crossgrades etc) then you should be able to transfer it.