Just to get a few things out of the way (my only credentials being someone who has spent plenty of hours dicking with N/A to boosted conversions and engine swaps in much simpler, much less electronically-intrusive older GM cars).
Stinger engine in an Azera: Right off the bat, the
3.3T engine is designed for longitudinal mounting and is not installed by Kia/Hyundai in any transversely mounted configuration. It's completely possible that all of the correct mounting bosses are already in the block, but it's also entirely unlikely. GM did this with the 3800 Series II for example, but it was also just a cost cutting measure since THAT specific block was shared between longitudinal and transversely mounted applications. This is not accounting for any other clearance issues, just simply the most basic part of physically installing the block in the car.
Transmissions: As long as the bellhousing is the same between FWD and RWD applications, it really doesn't matter. Physically anyway. Electronically is a whole different story. A RWD transmission isn't going to work in your setup. You don't have any choice but to use what's already in your car or some other electronically compatible Kia/Hyundai FWD transmission.
Bolting on turbo stuff: Again, the packaging of the
3.3T and it's manifolds, are designed for clearance around a longitudinally mounted configuration. I would be extremely surprised if you could simply bolt on the Stinger/K900/Gx0 manifolds and turbos and not have clearance issues hitting the firewall in the back or the radiator fans up front. This doesn't include all of the necessary fabrication for the exhaust.
At the end of the day: I'm a fan of sleepers, I completely get it. I own a relatively built FWD
Buick Regal that drinks ethanol and runs 12s. It's a laudable goal. However, I'm also in my 30s with no kids and I have a budget for bullshit that I know I'll never see any dividends from. I've learned a lot in 15 years of wrenching on shitboxes. I also don't need to drive the car every day nor do I rely on it for any serious transportation. My first go at this idea was when I was a teenager and knew barely enough to be dangerous. Same type of car, same engine, but with much worse results that consistently ended with me having an unreliable, nearly undriveable moneypit. The current incarnation of the
Regal wasn't cheap, and at the end of the day, it still can't go, stop, handle, or be as comfortable as my Stinger is. It's an utterly pointless car that I built because I'm probably having some bizarre early mid-life crisis and wanted to relive some dream 16-year-old Me had.
An additional two pennies: If you are truly bought into this idea and no one can change your mind, don't waste your time trying to play "junkyard legos" and attempting to get OEM stuff to work in this application. Read and learn everything you can about turbocharging and fabricate your own single turbo setup. Going about this trying to use the OEM parts is way more difficult than doing something bespoke.
But really: don't mess with your car. If you want something fast, get something that's fast (or at least designed for it) out of the box. Take it from someone who has been there, done that, and got the emotional scars/t-shirt to prove it.