I've created a villager breeder in 1.16 and i don't understand why the villager isn't throwing food, it's been well over 20 in game days and nothing, i tested this out in a creative world and it worked instantaneously. The villager just stands there doing nothing, the only day i've not had the chunk loaded was when i went on a mining spree, but that was only for 1 day.
(Edit: so after a while i saw that the villager was throwing carrots, but the villagers below weren't picking any up)
The only reason I know of that would make villagers not pick up food if they’re able to reach it is if the game rule mobGriefing were set to false. (I‘m not sure I remember the rule correctly.) I have no experience with farms though and only deal with free folk, so I‘m not the right person to give villager farm advice. I hope you have been able to solve the problem.