Check your search engine's preferences or settings page. DDG has /settings, G has /preferences.

Do you mean that "Google has settings called 'preferences' "? I have never set anything in Google. Where would I even look for that?

https://www.google.com/preferences => "Where results open"

(this is stored in a cookie, so if your cookies are cleared, you'll need to check it again)

Thank you. The Google setting for "Where to Open" opens in new window, not new tab. I do not want a new window. But I tried it anyway. I whitelisted google.com to allow it to set cookies. But no luck. Even with "open in new window" selected and saved, a new search still overwrites the contents of the current tab. NOTE: Since new searches had always opened in a new tab prior to the FF refresh, I refreshed it again, but that also did not help.

Okay, I'm re-reading this thread more carefully now.

We thought the problem was with the search result links, but those are working correctly, so the Google preference is doing its job.

You mentioned browser.search.openintab which is a preference for the classic short search bar which is an optional feature. See: Add the Search bar to your Firefox toolbar.

Unfortunately, Firefox has limited controls related to searching from other places:

(1) Firefox's address bar

You can direct ALL entries submitted through the address bar to open in a new tab (browser.urlbar.openintab), but there isn't a feature to directly only searches to open in a new tab.

(2) New tab page search bar

By default, entries into the Firefox Home / new tab page search bar jump up to the address bar, but even if you turn that off (browser.newtabpage.activity-stream.improvesearch.handoffToAwesomebar), there isn't a preference to send searches from this bar to a new tab.

(3) Search bar in a Google page

Firefox doesn't have a preference for Google pages. In theory, an add-on could modify the search form to add target="_blank" but I don't know whether there is such an add-on out there.

BINGO! See, I knew you were a genius - browser.urlbar.openintab is it. (I had misplaced my notes from last time I had to redo all my settings. Promise to do better this time) Many thanks for all the TLC!