To summarize, here is how the problems occurred over time.
About 9 or 10 months ago, after an update of the CC desktop app, it was no longer possible to organize my fonts. At that time when activating a font from the website fonts.adobe, I could still use it in InDesign.
But as the updates went on, the possibilities were reduced. Until the latest updates, where automatic activations from InDesign were no longer possible, nor from fonts.adobe website. It appears that website could not communicate with the app.
So, yesterday I contacted Adobe and a technician confirmed via remote control access to my computer that font management was no longer workingaat all.
I had no choice, so today I was forced to update Windows from Win10 enterprise LTSC 1809 to Win10 enterprise LTSC 21H2. By doing this upgrade, I now have the latest version of the CC desktop app and everything works normally.