Unpopular opinion: I'm happy that Zoe isn't this champion who has a lot of both offensive and defensive power locked behind a high-cooldown ult, unlike, say, Evelynn. The fundamental problem with that kind of design is that it often means a champion is dysfunctional right up until that effect becomes available to them, which then leads to these extended periods of time where you feel both incapable of killing champions properly, and unable to survive fights if things go badly, while your ult's on cooldown.
With that said, I do not at all think Zoe is a burst mage. She's this hypermobile champion focused on single-target damage, which is literally the definition of an assassin. It's interesting that when Riot set out to redefine the assassin class with Ekko, they ended up producing a skirmisher/light fighter, and when they set out to redefine burst mages, the end result is an assassin. It's also worth noting that she has a huge number of mechanical similarities with Evelynn's kit: her CC is delayed after application and enhances the damage of her combo, she gets this three-part set of proximity-based nukes after casting one of her abilities, and her ult, while not a nuke in itself, is designed to let her get in, deal lots of damage via her Q, then retreat. Only time will tell how Zoe will fare, but I think she's going to play much more like an assassin than a burst mage in practice, and I sincerely hope the M.O. for further "burst mage" designs won't be to give them a bunch of mobility.