Can finally reply:
1a. I couldn’t reply when my Apple-ID failed, after reporting my Desktop Stacks changed to 'Sort by Date' vs my setting of 'Sort by Kind.'
b. I followed the steps you advised, and found that the problem of 'Today' Folder always loading as 'Open' after every LogIn did repeat when starting macOS 13.6 in Safe Mode.
c. Also Noted that my Internet Security App didn’t load in Safe Mode, so that was ruled out.
d. I started in Safe Mode again, with all peripherals unplugged, printer etc > Still the 'Today' Folder loaded as 'Open.' (I don’t use a 'Guest' account, nor VPN.)
2a. In another article, for trouble shooting problems on a Mac, I was reminded to check in Activity Monitor for any unusual usage of CPU, etc, and for anything one didn’t recognize.
b. In Activity Monitor, I saw "NewsToday2" which triggered my recall of just days prior, in an online search, I’d been asked to Turn-On that same "Apple News Widget" in order to see the page I’d linked to. (Was this triggered by malware, or some false-positive acting like malware I’d read about in a Mac Blog, causing similar action? Of course, when I now search for that blog, I can’t find the posting.)
c1. Opening Notification Center drop-down menu, I saw the News+ App was loaded. Rt-Click I saw options to 'Edit,' or 'Remove' the News-Widget.
2. I used 'Remove Widget' > immediately the 'Today’ folder disappeared from my Desktop—only 'Yesterday' and other by-Date folders remained. >
3. Inside the Notifications Center, the box for News+ was gone.
4. Future LogIns of macOS displayed only the other by-Date folders.
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5a. Chose to try to add News+ Widget back to Notifications Center,, via Edit Widgets > clicked on News in Lft-Margin of Edit dialog > choice of 2 news articles displayed and would open. But I had to Drag them to the Notification drop-down > where ea displayed separately, and not within a single News-Box, as prior to Removal of News-widget. > Immediately the 'Today' folder appeared on the desktop again. >
b. Chose to Remove those 2 news-icons from the Notification Center and when completed > the 'Today' folder again disappeared from the Desktop ! > I concluded that the Apple-News-Wdiget had caused the problem on my macOS Ventura 13.6.
3a. I contacted Apple Support who assisted me in resetting my Apple ID, after my attempt to ReSet it had also failed.
b. Apple Support advised that I just go ahead with DLd and Install of macOS Sonoma, "it would correct any problems."
c. I did go to Restore-Mode and run FirstAid Tool from Disk Utility, to be sure my disk was clean, prior to DLd and Install Sonoma OS, via System Settings/Software Update (later).
(Apple Support thought the 'FirstAid step was unnecessary with macOS 14.0.')
4. Long ago in Ventura or Monterey versions of macOS, I’d removed the New+ Widget from Notifications Center. Whatever caused the Apple News+ Widget to be re-activated in my Notification Center, was that malicious code to get us to UpGrade as soon as possible when a newer macOS is/soon-to-be available? (Sometimes we have other pressing matters to attend to.)
5. So far, my problem seems solved by upgrading to macOS Sonoma, 14.0. Thank you for your suggestions.