At first I thought it was transmission noise, because it's normal to have a tiny bit of whine from it at low revolutions, however since it does it in neutral it's not. You can actually hear the transmission noise when it starts driving slowly and then this whine comes on top of that.
While I won't bother taking the car in, I am very tempted to go into the dealership later this week and make an absolute mess of a scene in front of other potential customers lol. Probably won't help things but it would certainly make me feel better after the useless service I have received lol.
Actually, that's the worst thing you could possibly do, especially if your expecting Hyundai to accept the car back. You're welcome to do what you choose but I'd advise against it. You just have to ask yourself; if I do so, will it actually service a good purpose. Honestly, it's going to cause you more difficulties.
I also got mad
once, a very long time ago thinking my personal kerfuffle would alert other owners or prospective owners. Did nothing but make me the arse and the one with a chip on my shoulder. Otherwise, the intentions were crap and it didn't accomplish anything. Didn't make me feel any better either. Just reminded me of how stupid it was.
The components that must be removed for access to the transmission removal are;
the entire front end, undercarriage and engine and all attached components.. If they didn't align the clutch properly on reassembly, you'll get this type of noise. The bump or bang is very possibly one of the heat shields on the exhaust.
However, when you remove the engine and transmission, there's always a possibility or clearance issue with heat shields and other engine items that were remove to gain access to the transmission. IE., fuel line attachments, hoses, emission components etc. making contact with the chassis. There are a plethora of lines and electrical connections that need to be secured properly with assorted OEM zip ties and clamps.
Personally, I believe your dealership service is near incompetent and lacking. When the tech drove the car, the tech didn't want to analyze the whine or the bump. Just like with the transmission gear engagement and clutch cables issues you experienced. They're not doing the diligence required. Get it in, get it out as fast as possible, don't worry about the QC'ing of the worked performed.
I'll also, second the axle tramp or wheel hop that's already been suggested;
if an underbody suspension components were not installed correctly and properly torqued.
Turbo whine is most likely a piece of foreign debris that has dislodged in side the turbo housing or a bent blade. Most times service departments don't take the time to cap off or block vital parts like the Turbo inlets, oil & transmission line etc. They just let them dangle and stay open to debris contamination. Yes it's BS and causes additional problems later on during reassembly and for the owner. They generally don't take the do care necessary to protect the subsystem components.
If it were mine, I'd take it back to another dealership, other than the one it came from or is now being utilized. Such bad service and mechanical incompetence, is truly alarming.
I ran into this with a Nissan Dealership once and it was a nightmare of mistakes, damage, and inconvenience.
Sorry about all the issues and I wish you all the best in whatever you decide
.
MERRY CHRISTMAS!