Creative Cloud app won't download the latest version of an app, reports incorrectly that I'm "up to date"

I'm reading that there's been a version 16 of After Effects for some number of months.  I'm running 15.1.2.  The Creative Cloud app seems to feel that this should be good enough for me; it identifies 15.1.2 as "up to date", and won't download the more recent version.  I have suggested that it "check for app updates", but this produces no different result.

At the risk of sounding cranky, I can't help but feel that it would be lovely to have the latest version, since I am paying for it on an ongoing basis.  I'm tempted to also share my feeling that it would be nice to get actual support from Adobe in exchange for my actual money, but I fully understand that that would be shouting into the void.  Anyway, if any of you good people knows what can be done about this, I'd be very grateful if you would clue me in.  Alternatively, if anybody knows any good jokes about how renting software is better for the user than buying it, because you're always up to date, I'd love to hear them.  Thanks in advance.