"my granaries are not accepting any food. actually, no cart pusher has tried to take food (grain) to a granary, but instead always unloads it at a storage yard"
Storage yards have priority. Change the granary to GET some amount and it should work. Bazaar ladies will only buy locally-grown food from a granary.
I normally set at least one SY to accept ¼ to avoid drowning cartpushers.