Zoe is just fucking weird.
Her passive is basically Lich bane.
Q is suppose to be her main damage spell that is able to nuke people, but playing against it doesn't feel fair (its also super fucking frustrating) so Riot kind of wants to keep it undertuned or its basically broken.
W is an ability that really punishes the enemy players for using their SS while also giving her damage for using summoner spells with no cooldown while not having to aim it, while also giving her a MS boost. Also RNG drops from certain minions, which is... weird because SS and item abilities can completely change a lot of match ups. The W damage is either barely noticeable or too much because she doesn't have to aim it and the movementspeed boost lets her get into a position to damage you with it.
E has aspects of counterplay to it, but also feels forgiving because of the lingering zoning hitbox it leave behind if she misses. It also deals true damage for some reason when someone pops the sleep... Which is weird...
R exists as a way to let Zoe land her (and do more damage with) Q and E easier.
Two things happen with Zoe.
Either her Q does an absurd amount of damage and she's basically Old Nidalee without a reliable escape or her Q doesn't do enough damage and she's kinda there with some pick potential with E.
And if her Q doesn't do enough damage they put damage into her W, which makes her hard to deal with (also technically hard for her to control and point her damage at enemies I guess) because she gets free damage from using summoner spells, while gaining a lot of MS and also giving her a bunch of RNG from balloon minion drops.
My goal here isn't to just state her kit or call her overpowered but to clarify her kit is incredibly hard to balance by design because her damage comes in either Q (which to be useful has to absolutely chunk people from far away) or her W (which gives her a bunch of shit depending on the SS, the MS and can be unreliable because RNG and auto targeted damage).
Like half her kit calls her to be this kind of auto attack spellweaver who wants to throw autos in between every ability, to take SS from enemies and use that to gain an advantage while being in their face and the other half calls her to be an artillery mage who oneshots people from afar.
Zoe's kit is this weird mix between long range poke/burst and battle mage and it causes her to be a big balance issue because the two playstyles don't mix together very well.
I'm sorry for the big wall of text and also if it doesn't make sense (because I'm writing this at like 12:00 AM) but those are my thoughts on Zoe.