You know, the first thing that comes to mind isn't a pure dystopian novel, but it fits your ask perfectly: 'The City We Became' by N.K. Jemisin. Okay, maybe not a traditional heist, but the core action is a team of unlikely heroes executing a complex, multi-layered plan to steal the literal soul of a city back from an interdimensional entity. The setting is a near-future New York under siege, feeling deeply dystopian in its fracturing reality. The planning scenes where they figure out how to use their unique powers and the city's own landmarks as tools? That's heist logic through and through.
Another one that scratches that itch for me is 'The Library at Mount Char' by Scott Hawkins. Again, weird book, but the central plot involves a group of adopted siblings, each a master of a strange catalog of knowledge, orchestrating a long-game takeover of a godlike figure's domain. The dystopia is more of a cosmic, rule-broken one, and the elaborate nature of their plan, with misdirection, sacrifice, and hidden objectives unveiled piece by piece, feels very much like a high-stakes heist movie, just with... well, more lions and necromancy.
For a more classic take, I'd be remiss not to mention 'The Dark Forest' by Cixin Liu. The entire Trisolaris Crisis premise forces humanity into the ultimate long con against a superior alien force. The 'plan' involves hiding the true nature of human strategy across centuries, using societal and technological development as misdirection. It's a heist on a civilization scale, and the dystopian elements of global surveillance and forced conformity under the threat of annihilation are palpable. It’s less about stealing a thing and more about stealing a future, which somehow feels even bigger.