AutoCraftingTableBlockEntity has this code in its canMake method

		DefaultedList<ItemStack> remainingStacks = recipe.getRemainder(crafting);
		for (ItemStack stack : remainingStacks) {
			if (!stack.isEmpty() && !hasRoomForExtraItem(stack)) return false;
		}

		return true;

This is wrong, e.g imagine 15 empty buckets in the remainer and three milk buckets in the cake recipe. The method will not return false. Also doesn't work if there are two different remaining types, like a bucket and a glass bottle from a honey bottle for example. I think this never happens in vanilla recipes, but could easily in mod recipes.

I tried it with the cake recipe and the machine simply doesn't work when there are 15 empty buckets and I don't get why

Buckets stack max size is 16 ;)