If I can't fix the studs on the existing wall how can the wall remain upright?
You attach it to the OTHER inner-leaf walls, and the inner-leaf ceiling. Since those are all at right-angles mutual to each other, they provide the support to keep things together.
Of course, if you don't plan on building the other walls and ceiling, then you have a problem. But on the other hand, if you don't plan on doing the other walls and ceiling, what's the point of doing anything? Isolating one single wall of a room is like trying to build an aquarium with only one pane of glass....
I've seen wood framing wrapping all 4 walls and ceiling do that but is it possible to do that with lightweight metal profiles?
If you can do it with wood framing, then you can also do it with metal framing.
Since I don't have the space to spare and build a complete room within a room wood structure that supports itself, maybe the use of resilient channel or genieclips on the drywall would help flanking?
If you don't have the space to build a proper room-within-a-room, then you don't have the space to get good isolation. You cannot get around the laws of physics by hoping they will go away!

Either you sacrifice the space you NEED to get the isolation you WANT, or you don't get the isolation. It is that simple. There are no magic products, materials or techniques that defy the laws of physics. Acoustic isolation REQUIRES space, and mass, and damping, and decoupling. If you don't have that space, or don't want to add the mass or damping or decoupling, then you cannot get good isolation.
From what I gather it will be close to impossible to achieve better isolation for low frequency response considering the limited space I can spare for a massive construction or bigger air gap
Correct.
Maybe something like this to isolate the metal studs from the masonry wall:
That will provide LIMITED decoupling, yes... but how do you plan to attach the ends of that wall to the side walls and to the ceiling? And how do you plan to stop the flanking noise that is already in that wall from getting into the OTHER walls of the room and the the floor, and the ceiling? Your new wall would reduce some of the airborne sound that is being radiated by that wall, but will do nothing at all to reduce the structureborne sound that it is passing on to the walls on each side, and the ceiling, and the floor.... That's why you need a proper room-in-a-room.
"Nonload-bearing metal studs are sufficiently resilient and do not improve with a resilient channel." Wouldn't this mean that the lightweight metal stud I am using to frame the partition drywall is resilient enough?
Your link does not work: it does not go to a PDF. The claim is also strange, since it does not agree with laboratory test results, or theory. In any case, even of that were true, it would not apply in your case since your proposed method does not allow your metal studs to act resiliently...
Your floor plan is fine: That should provide a little extra reduction in sound transmission.
Your ceiling plan will probably also work reasonably well.
... provided that you also solve the wall problem.
- Stuart -