How do I get a GtkComboBox(Text) to hexpand within a GtkToolItem? - gtk

Question

I'm trying to embed a GtkComboBoxText in a GtkToolbar (think URL entry) through a GtkToolItem. It's the most important part of the toolbar, so I'd like it to take as much space as is available.
I've tried setting hexpand to true at many various levels of the container chain, from toolbar to GtkComboBoxText (example below) to embedded GtkEntry and GtkCellAreaBox though every intermediate container I could find a handle to.
Highlighting with the inspector, it looks like the toolbar is ok with taking all the horizontal space, but not the toolitem, no matter what it contains. But that's guesswork.
(my code's Haskell, gi-gtk-3.0.37, dynamically linked to gtk3.22.30, but I don't suppose that changes anything)
main :: IO ()
main = do
Gtk.init Nothing
win <- new Gtk.Window [ #title := "win" ]
on win #destroy Gtk.mainQuit
vbox <- new Gtk.Box [ #orientation := Gtk.OrientationVertical ]
#add win vbox
hbox <- new Gtk.Box [ #orientation := Gtk.OrientationHorizontal ]
#add vbox hbox
f1 <- new Gtk.Label [ #label := "filler 1" ]
#add hbox f1
cb1 <- new Gtk.ComboBoxText [ #hexpand := True ]
#add hbox cb1
f2 <- new Gtk.Label [ #label := "filler 2" ]
#add hbox f2
tb <- new Gtk.Toolbar []
#add vbox tb
f3 <- new Gtk.ToolButton [ #label := "filler 3" ]
#add tb f3
tbi <- new Gtk.ToolItem [ #hexpand := True ]
#add tb tbi
cb2 <- new Gtk.ComboBoxText [ #hexpand := True ]
#add tbi cb2
f4 <- new Gtk.ToolButton [ #label := "filler 4" ]
#add tb f4
#showAll win
Gtk.main
I'm aiming for results similar between the hbox (above) and the toolbar (below).
Is this kind of behavior possible? Am I using GtkToolbar wrong?