How to seal edges of plumbing work for noise isolation.

Single glazing with storm windows absorbs sound reasonably well, I would not expect a huge decrease in sound level with triple glazing, but certainly not an increase. Single glazing alone is another story, it's sound absorption is terrible.

The increased sound is certainly due to the frames and adjacent construction. While there is often a correlation between thermal loss and sound transmission, sound is much trickier to manage well. It is sometimes counter intuitive. The construction joints must be carefully detailed. The general concept is to avoid any solid connection between inner and outer surfaces. Any connections should be via resilient, absorbent materials. Typically, you want to fill any voids with sound insulation, though in some cases this has been worse than a simple air gap.

Also consider exterior sound attenuators. Walls, fences, trellises, large shrubs, trees, berms all will help attenuate sound, but when you consider cost vs. benefits, such measures need to be carefully considered.

You don't need both quiet rock and green glue, they should be seen as alternatives. Also you're going for higher frequency noise: footfall or low frequency noise would be a different answer.

I'd do this: identify and mark stud locations, have a contractor drill holes and dense pack insulation into the wall (see video), patch the holes, find your marks then green glue and screw 5/8" drywall and be done with it. No framing needed.

But your next problem is likely flanking: sound coming through the floor, heating ducts, over the top plate of the wall, out and back in a window, etc. You'll likely still hear that TV without some pretty detailed work to find all the paths.