I'm having a similar problem, started a couple of days ago. The search field is missing, and when I right-click and choose "Customize Toolbar" or View > Customize toolbar the icons in the toolbar wiggle and can be dragged, but the pop-in menu that allows you to configure the toolbar by dragging elements into place does not appear. The only way to get out of the "wiggling icon" state is to close the browser window and open a new one.
The search field was visible as an outline, until I dragged it off the toolbar, at which time it disappeared. However, even when the outline was visible in customize mode, it did not appear in the toolbar when using it normally.
I created another account (with admin privileges) and logged in, and Safari worked as expected. So it must be something with the local configuration.
Any thoughts would be helpful, thanks!