Paul writes
I read that for broad beans you should dig the roots into the ground
(something about nitrogen?). Does this apply to runner beans too?

All sorts of peas and beans. Things in that family are able to 'fix'
nitrogen via nodules on their roots, therefore the roots are full of
nitrogen, therefore worth digging in to improve the soil. Clover is in
the same family, but I'd be worried about digging that in in case of
getting overrun by it.
--
Kay