I think the explanation is the following : my Adobe Enterprise ID does not include access to Adobe's Document Cloud, most probably for data protection reasons. Is there a way to get back to the previous, purely "local Hard Drive", system ? If not, it would be a good idea to let users of future versions specify which way they work : with or without signing in the Document Cloud.

Acrobat retains the signed in state until manually sign out is triggered.
By any chance, are you signed in on multiple devices? If you cannot retain the sign in status, please attach a video of the same and revert.

Thank you. This was my guess too. I'm always surprised that data on clouds is considered better protected as far as privacy is concerned, than on the local hard drive, but anyway...
Is there a way to be automatically connected at startup, instead of manually ? I don't have to log on Creative Cloud with the other apps. Why is it so with Acrobat ?

From the screenshot shared, i can see that you are signed out. In our latest update, we have implemented a feature where in if you sign out, all the files in your recent file list will be cleared out to meet privacy concerns.
Once you sign in, you should be able to see the cloud files though. Could you please confirm if you can see the same?

MacOS 10.15 Catalina
Acrobat Pro DC 2019.021.20048
Adobe Enterprise ID (eric.pebret@sncf.fr)

It appears that the list is not actually emptied at startup : I have tried closing the app, then the OS, and it still shows the files I opened this morning (see scrennshot). I can no longer see any of the files I opened last week, or the weeks before, though (wherein all my commonly used files could be easily found, using the search function).

This part of Acrobat's previous versions worked perfectly fine, I can only regret them...

Can you please share the following information to help us investigate the issue:
1. OS platform WIn/Mac?
2. Acrobat Version screenshot
3. Are you signed in?
4. A video capturing the workflow