[name_f]Avery[/name_f] seems like a good choice, since it’s the only one you don’t seem to have hesitations with!
That said, you might be slightly overthinking it – which is normal when choosing a new name! But I’ve never heard of a [name_f]Harper[/name_f] being called Harpie as a nickname (surely the relation to the word harpy would deter people from using it?). I’ve never heard of a [name_f]Harper[/name_f] getting her name nicknamed at all, but there are other, more pleasant nickname options, like [name_f]Harrie[/name_f].
As for [name_f]Bailey[/name_f], it doesn’t make me think of alcohol! It helps that the alcohol brand is Bailey’s, not just “Bailey” on its own. It’s not like naming yourself Vodka – [name_f]Bailey[/name_f] started as a name and not as the name of a type of alcohol, which I think is obvious in the case of the alcohol brand too. [name_f]Bailey[/name_f] is my favourite of the 3 personally! I think it sounds friendly and laid-back.