Which expansion did they get right, and why?

[Absurdity]

Stormblood feels like the last expansion where they bothered doing creative things with instance and fight design (like the minigame phases in the Four Lords trials, or things like St Mocianne's Hard dungeon having extra/optional mechanics like rinsing off mobs, or that one mob that can transform other enemies if you get them in its AOE cast). It's also where we got Eureka, the Ivalice raids, and in general a pretty wide host of interesting and creative content.

Shadowbringers... narrative wise, they got it "too" right I think, to the point each expansion we've gotten after it has just been rehashing the core concept of ShB and trying to recapture the lightning in a bottle it was. Felt like EW was rushed and unsatisfying? Not a fan of how DT turned into "oops yet another apocalyptic event involving yet another shard and also our 3rd final dungeon with the villain narrating us through a flashback"? You can thank Shadowbringers for that!

Pretty much this.
People always gush about Shadowbringer's story but I consider it patient zero for the rot that has settled in this game.
As you said it is the reason for every MSQ following a similar template, but it's also the start of the incredibly stagnant job and fight design.

Funnily enough when people say "Stormblood story bad" they always tend to ignore the patch story from 4.2 onward. Building up Garlemald as more than just vague bad guy empire and giving us a glimpse of the political intrigue and factions within it...which was then completely sidelined in ShB and thoroughly destroyed by Endwalker, along with any remaining old story threads.