Take a look at the post by H3Nutcracker on previous thread page (10). The picture marks which numbers to edit.
The information in the appmanifest is divided into parts that correspond to how the game is downloaded. Each part begins with an ID for that part, you need to find that ID in SteamDB and check that the Manifest ID matches with the ID in the appmanifest. If not, you need to replace the ID with the Manifest ID from SteamDB.
As long as you keep the appmanifest read-only (when Steam is running), that's all you need to change.
There will likely be at least one more update before they think they are done. So keeping the manifest read-only is really important. At least until F4SE/related have caught up with the changes since many mods rely on it.