Pages appears to quit when closing document

I cannot help, but I am "happy" to have finally found some one who seems to have the same problem that plagued me for now a week.

I have an imac 2019, Mac OS 10.15.7, and Pages 11.1

As to my part, this same exact problem appears not only in Pages, but with all iWorks apps, and also with Preview, Calendar, and Messages.

I have called Apple Assistance two times, and go one time to a Genius Bar. All three Apple employees to whom I have spoken, but one, seems not to understand this problem.

According to them, I have only two choices, either reinstall the OS, or upgrade to Ventura. I does not do any of them, as to now. And I see that upgrading to Ventura would not resolve the problem, since you are under Ventura and you have the same exact problem, at least for Pages.

Before this problem be a constant one, as to my part, the "faulty" apps had begun to bounce in the dock for a long number of seconds when trying to open them. As to Pages, I have also lost access to all my templates, and had to recreate them.

As for my part, I hypothesize that the problem comes from icloud, because after I have disconnected from icloud and icloud drive, the bouncing problem disappears, but the app (Pages for exemple) begin to show no active in dock after a few seconds, when no document was not open, but opening Activity Monitor, it shows Pages is still running.

My other hypothesis is, that it comes from software update, because I have received update messages during the bouncing problems happened, for pages, numbers and keynotes, and because I am still on Catalina, iWorks apps could not be updated.

If you click the red title bar traffic light on an open Pages document, that closes the document but does not quit Pages which continues to run in the background. The dot beneath the Pages Dock icon remains, after switching to Safari, the Finder, or another random application. If you do not want Pages to continue running, it is best to formally quit the application.

Tested: macOS 13.2.1 and Pages v12.2.1.