Installed apps not showing in CC & licence expired

Running Adobe CC for teams.

We've had Adobe Illustrator, Indesign, Photoshop, Bridge and Acrobat installed on two Macs for years. One of them was recently replaced and restored from a Time Machine backup. I've  signed out of CC on the now defunct Mac. Everything seemed okay on the new Mac until yesterday when I installed the latest version of Illustrator. I noticed that the installed apps list in CC didn't list any of the apps that were on the Mac - apps that I use all day every day.

Because I couldn't therefore update the installed Illustrator, I decided to install the latest version afresh. This installed correctly but when I launched it for the first time it informed me that my illustrator licence had expired and I had 99 days to use the app. It told me that "You’re currently signed in with your email ID XXXXXXXX. You can also sign out and use an Adobe ID that already has a paid subscription." The problem is that I already have a paid subscription that is associated with the Adobe ID!

I've signed out of CC, rebooted the Mac and signed back in but nothing has changed. So, two-fold question:

How do I get CC to recognise both my already installed apps and also the fact that I have a paid subscription?

Thanks in advance.