Currently, every time you interact with the address bar, the search engine that gets used is always your default search engine (unless you manually change it). Even if you just used an alternative search engine in that tab and the search text is still in the address bar from you doing that.
Since the search text in the address bar, the search engine should be remembered as well. Otherwise, it's not really analogous - simply selecting the text and hitting enter again without changing the text at all will send you to an entirely site if you were initially searching on a non-default search engine.
I personally use my alternative search engines a lot, and I get tripped up by this behavior all the time. I can't even tell you how many times I've searched, realized I made a typo, went to fix it, and as a result, accidentally Google something instead when that wasn't what I intended, and then had to go back to the address bar yet again to specifically select the same search engine I had used the first time.
The search engine change I'm suggesting is ephemeral. It doesn't actually change your default search engine or affect other tabs. Even in the tab in question, if you navigate away from the search page, it should go back to using your default search engine, because the address bar stops keeping the search text if you do that and it's easy to remember "oh, the text is gone, I need to reselect the search engine if I want to search again".
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