If you give a stone to an allay, and then drop a stone beside it, of course, the allay will also pick that up, but it only deliver you one stone (expected two since I gave it two)
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WAI per change log:
Allays will collect all the surrounding items that match the item they are holding
Allays will like a player who hands them an item and will bring the items they collect to their liked player
– https://www.minecraft.net/en-us/article/minecraft-snapshot-22w13a
Only what they collect, not what is handed to them
Allays will maintain their held item unless it's taken away from them by the player. In other words, they will not throw their held item away when delivering items that it has collected. The behavior as shown in your video looks normal and no issue seems to be apparent. I'm pretty confident in saying that this is working as intended, though I don't have a source to reinforce my claim here.