Hello

Since Firefox 122 https://bugzilla.mozilla.org/show_bug.cgi?id=1852044

The Search bar can be activated from the Customize Toolbar menu.

Add the Search bar to your Firefox toolbar. https://support.mozilla.org/en-US/kb/add-search-bar-firefox-toolbar

But that's not what's happening here. Here's what my browser shows when I select "Customize toolbar":

Notice the LACK of the "Search" option! There's only "Find".

Could you check whether it slipped into the overflow list? That's a box on the right side of the Customize panel.

Nope, only thing there is Firefox View.

Of course, it's not the answer expected, for confirmation, Search, is available. I cannot reproduce your malfunction, for my part, I don't know what else to tell you, sorry.

Well, I got it back somehow-- when I hit "Restore Defaults" the search bar option reappeared in the drag-and-drop area. (Then it disappeared from that area after I put it on the toolbar-- maybe because it can only be there once?)