I have fixed the issue. I somehow magically found myself back on the Package Management OVERVIEW (not download) page, and realised that the two plugins that are sitting there quietly have a tiny green "install" button on them. Unbeknownst to me that, once having downloaded the package successfully (I can only assume from the progress bar that briefly flashes on the screen), one is actually supposed to take oneself back to the Package Management overview page, and hit that little green button.
JFC.
Please leave this up in case anyone else has such UX problems.