@twolff-wescale If it works in a standalone installation, but not in a regular installation, that implies that there's something messed up with your Opera profile for the regular installation or that something external is interfering with Opera when it's install in its default location.
Well... As Mac-2 is on the way to repair service, I decided to purge the HD and reinstall the MacOS operating system, altogether. With Mac, its not such a big deal as with Windows. But one only needs to do it in very rare occasions - like now, when I'm testing a heating problem of Mac-2.
After the OS was installed, I downloaded Opera and logged into sync. And now I can see all three devices - Mac-1, Mac-2 and Windows-PC open tabs, bookmarks and speed dial.
I guess we can call this case solved, even though we don't know what caused the problem, initially. Thank you @lecog for your help, and let's carry on from here. Have a great summer and stay healthy!
Ok, so let me ask this, instead. I gather, from the lack of any responses and my own searching, that there is no extension that does what I need. So I'm willing to try and do one, myself. There's just one thing I haven't been able to find (or know that I've found it in a list of extensions related to bookmarks): how to basically intercept a user opening a bookmark, whether it be in bookmarks, the bookmarks toolbar, etc., and, using code that I have found, open that bookmark in a new tab? I just need to know how to see that click on any/all bookmark(s) and act on it. Suggestions? Thanks.
Well, just to close this question and topic out it seems that the problem was a combination of operator error and late night confusion over the results. My bad but at least I opened an account here so I can post on forums in the future and figured out how to use Bookmarks better.