Although I have found partial and indirect answers to this question (see, e.g., this link), I am posting this here because putting together the bits and pieces of the puzzle took me a bit of time, and I thought someone else might find my efforts of use.
So, how to achieve a seamless resizing of images on buttons in GTK+ when the parent window is resized?
The solution offered for PyGTK in the link posted in the question does not work in Python-GI with GTK3, although the trick of using a ScrolledWindow in place of the usual Box was very useful.
Here is my minimal working solution to getting an image on a button to resize with the container.
(The -10 on the width and height are to accommodate the inner borders and padding in the button. I tried fiddling with this to get a bigger image on the button, but the result did not look so nice.)
The jpeg file used in this example can be downloaded from here.
I welcome further suggestions on how to do this.