So, taking this one step further.
Preview, to take one app, is not updating the list of files in the Window menu. The Window menu shows a list of open PDF files, ten in all. Like with my Safari tabs, I delete the files that I no longer need to read, and leave a couple that I'm actively using. I then Quit and reopen the app, or reboot and on opening all ten files are back in the Window menu list, and are, just as that shows, open, even though they were closed. I seem to be having a bad episode of Groundhog Day, in all my apps!
When I look at the Open Recent.... list in the File menu in Preview, it shows the files that I closed. I think this is behaving correctly. When I open a new pdf file, it also appears in this list. When I close the app and reopen, the new pdf file still shows in that list, though it disappears from the Window menu list (ie. it closes without me closing it). The Window menu list goes back to the Groundhog day list of the ten open files. That new file also shows up in Finder's Recent Folder, which is set to "Raw Query""=(kMDItemLastUsedDate = "*") &&. It doesn't show up as the most recent file used though.
Following advice here: how to clear recent items from Preview's menu in Dock
I moved com.apple.Preview.LSSharedFileList.plist" from ~/Library/Preferences to the Trash and rebooted. Note that the Preview recent items list in Dock, shows the same recent files that I see in the Recent folder in Finder and in the File>>Open Recent... list in Preview. In any case. the plist file was not recreated, and the behaviour did not change. I suspect that in Preview at least, my problem is not Recent Files, but the Open Files and the Preferences updating. So, my action was pointless, but made out of desperation! If there is another plist file that I should be recreating to fix this, please advise?
Anybody have any further ideas on why the Safari tabs are not staying deleted please? I can show that there is similar behaviour happening across a range of apps, such as Preview's failure to update the Open files list in the Window menu, so this is possibly something systemic.