You are welcome. Coming here or at forums and talking about problems helps, we should always do that.
I won’t close it though, since the 'What’s New' screen, once closed, should never appear again, until the next major update at least...
Please comment back if it ever pops up still.

Egor Chistyakov: Thank you very much for your persistence and help at disabling the nuisance that would otherwise have kept bothering me.

Good job!

That mish-mash is called Home Screen, and you can disable it in Preferences, with 'Show The Home Screen When No Document Are Open'.
I don’t like it myself and always have it disabled.
As for the 'What’s New' being that obtrusive — I have no idea why it behaves this way. Despite me having the badge — I am a user just like you. It’s up to the team to figure out what’s happening. So far you are the first one who reported this, that’s why I try to get as much details from you on the behavior, to help to investigate it and just help others who might find this.

Now when I "close" the splash has changed to the "mish-mash" that I alluded to last time. (See attached screen shot.) Again, when I hit the close button, why not just close and take me to the Desktop. Why all this annoying In-Your-Face clutter?

...but does it make this thing I called 'dialog window' and you call 'splash' to stop being called when a doc gets closed after you click-through all the items with this button?

Right. When you wrote "this dialog" I thought you meant this discussion. I had not before pushed he "Next" button in the splash screen because I am wary of rabbit holes. Sure enough, when pushed, the button takes me down a hole of advertisements and ends up at another confusing mish-mash of options that just distract from my desire to close and get back to the Desktop. Very annoying.

Strange. It’s there in your own screenshot. Take a look, I’m pointing at it with the mouse.

I do not see a "Next" button in the lower left corner of this dialog, nor anywhere else.

Nor could I find a Preferences setting to prevent the annoying splash screen.

Richard, this dialog has a 'Next' button in the bottom left corner. I meant you trying to click through all items in the list this windows has, to test if this somehow makes it stop from spamming you.
I understand your frustration exactly, and I don’t offer this as a final solution, and I can’t do anything like it. I just want to see if it helps you and provide the team with anything they can use to troubleshoot it.

I don't know what you mean by "Next button." I've never noticed a "Next button" in the Illustrator interface.

But the point is to make ONE click and have the document closed and be back to the Desktop. Any "click-through" sounds as cumbersome, if not more so, as having to click a second time to get the splash screen out of the way.

Interesting... Just in case — does it help to not close it, but click-through all sections with Next button?

Screen shot attached. When I close a single open Illustrator document, or the last of more than one Illustrator document, the attached annoyance appears. I rarely have more than one illustration open at a time, so it appears nearly every time I close.

Richard, what 'splash screen' do you mean?
I get nothing when I close a document, other than a save dialog if a document was unsaved.
Can you share a screenshot, please?