Tested but no, these ideas were not the solution.
Cleared all cookies and relaunched to be sure but no change in behaviour.
I won't switch to "Block cookies> Always" though, because I need to retain that so that my preference to "not save passwords for this site" remains on (a dumb loophole by Apple, in my opinion, that to play it safe I have to delete my preference to ask to play it safe every time I visit the same website).
"Prevent search engine…" switched on changed nothing with the familiar "Bookmarks and History" list that pops up while typing a URL. Although, I didn't realize that switch was there, so thanks. I've often wondered how I stop Google from interfering.
This gave me another idea, but testing also failed. When searching for examples, I speculated that maybe Spotlight and Safari were sharing data, so I turned off web sites in Spotlight preferences but that changed nothing except to remove the search result section from Spotlight.
This brought up an entirely new question that might be related: Where is Spotlight getting it's "Webpages" results from if they don't exist as files? Does a "Webpages" found by Spotlight represent only a ".webloc" file, or do all those file types appear under the "Documents" section of search results? Duh, I can test that - I just did with a known file and ".webloc" file types appear under both sections.
So, what is a Spotlight result that appears only under "Webpages"? Right-select renders the web page referred to, and select launches Safari to the original site. Wait! If it's in the file system I should be able to find it with that Finder thingy! Finally, I found my working example, along with 3,579 others, under "username/library/Caches/Metadata/Safari/Bookmarks" as ".webbookmark" file types, offering up a concrete question:
This simply has to be where the "Bookmarks and History" suggestions are coming from. If I'm deleting my bookmarks, manually or resetting, then what are those thousands of items in that bookmark folder doing there? Alternatively, is there yet another privacy setting that refers explicitly to that directory?
I figured it out, and of course it's embarrassing. Those 3,579 bookmarks were manually archived by myself, amongst which I found my specific test URL.
I did this back when I was shuffling boot drives after buying a new mini. Basically, it never occurred to me that the manually-created folders were being referenced and not just "Collections". For that matter, I have about 50 URL under "Bookmarks Menu" that I never use. In plain English, the URL suggestions have nothing to do with history as they're coming from real bookmarks.
I only go back to the Bookmarks sidebar where my common sites are organized categorically, or launch frequent fliers from top sites. Unfortunately, bookmark subfolders aren't indexed and search only finds bookmark names - anything more than one folder deep turns into a rescue mission to locate, and a healthy reminder to not let old bookmarks get out of control in the attic.