Created attachment 155270 [details]
Example of the GtkToolbar implementation.

When opening the search bar in a chat window, the window is forced to be at least a minimum width of the search bar. The search bar itself could be viewed as a little wide for a chat window initially, but if you start typing and the phrase isn't found, the indicator that no phrase has been found widens the window quite a lot more.

It appears that Epiphany handles this by using a GtkToolbar, which automatically provides a menu button for items that don't fit in the given width. I tried this and, at least with my theme, it looks kind of ugly.