It is called primary-toolbar style because it should be applied only to primary toolbar.

In Gtk, toolbars by default can hold only ToolButtons, but there is the ToolItem class, which does not have a visual represntation.

That is created because it can embed other widgets.
ToolItem has add method which you can use like :

my_tool_item.add(my_box)
where my_box contains your entry

Then you can add your tool item to toolbar
my_toolbar.insert(my_tool_item,index)

Your toolbar of course has called :
get_style_context().add_class(Gtk.STYLE_CLASS_PRIMARY_TOOLBAR)

The reason why you cannot use "primary-toolbar" with non Toolbar widgets is most probably because in .css files it is defined like :

GtkToolbar.primary-toolbar 



{



    /* style info*/



}