What you describe is default for me. I can type “test 123” in the URL bar, which looks up that phrase with my default search engine, and if I select it again, I can edit or copy the original search query “test 123”. It doesn’t show a URL. You can configure that setting on the settings page where you can configure your default search engine.
I just created a new profile and it isn't default on it. What settings do I change for it?
You can use the reverse of this (scroll down to the 3 steps): https://www.ghacks.net/2022/12/23/firefox-may-soon-display-the-search-term-instead-of-the-search-engines-address/. If you don't have that option, I think you might be running an outdated version of Firefox.
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