He is shown to be extremely competent in combat, but that extraordinary competence doesn't generally spill over into some magical "get out of jail free" at every turn.
I haven't read the book so I certainly can't claim otherwise, but the synopsis has him, over, and over, and over, and over again, achieving what was not possible for
anyone else, succeeding where
all others failed, making friends with
everyone who is cool, saving his friends when it counts (so claims the synopsis), and so on.
The rest of what you're saying just tells me the setting is probably grimdark. Lots of genuine fanfiction Mary/Gary Sue/Stus also fail to save their friends where it makes things more dramatic for them.
If Vaelin Al-Sorna is a Gary Stu, then so is Aragorn
Well yes, Aragorn absolutely would be in the general Gary Stu bracket
if he was the actual hero/main character of LotR (but Tolkien didn't always like Aragorn all that much, to judge from his letters, and intentionally kept him from being front-and-center), and frankly from the synopsis, Vaelin makes Aragorn look like a small toddler by comparative competence at, well, pretty much everything.
Personally I don't hold too much to the Gary Stu/Mary Sue thing outside of fanfiction (where it has a more precise meaning), because it is a bit overused about any heroic character, I'd generally only bring it up if you get into
Wise Man's Fear "I trained as a ninja and I screw all the hottest babes also I am the best at sex because the sex-god taught me through sex" kind of "Jesus wept..." eye-roll territory.
If the synopsis is correct, Vaelin is a more
overpowered character even than Kvothe's claims about Kvothe in a darker setting/universe (which is not uncommon), but probably less
annoying that Kvothe's portrayal in WMF!
(I appreciate you saying this. If you dig far enough back in the ratings of
Wise Man's Fear on Amazon, like, ALL the way back to March 2011, I was one of the first and earliest 2-out-of-5 star ratings of
WMF basically saying exactly what you're saying. I loved
Name of the Wind and utterly despised
Wise Man's Fear and basically will never read another written word of Rothfuss's ever again. But you'd never know what you're saying is true based on the 70,000 5-star ratings of the book on Amazon.)
Oh I get that the 5-stars can be galling, but look at it like this - pretty much anyone who has the slightest modicum of good taste probably thinks Terry Goodkind is a mediocre to outright terrible writer and most of his books are mediocre to truly appalling and depraved. You can pretty much objectively demonstrate how bad his writing is on a variety of levels, not least that a lot of it is psychotic blood-soaked political polemic/wank fantasy. Yet the first book in his series,
A Wizard's First Rule has 4.6 stars on Amazon. Sure
Wise Man's Fear has 4.7, but like, you can take some solace in that it has virtually the same scores a truly terrible, utterly generic book about a man called "Richard Cypher" who at one point uses the "special mode" of his "magic sword" to ritually kill a sexy BDSM/torture nun in a bed (who wants to be "killed" with his "magic sword" in bed, you understand). Indeed
A Wizard's First Rule remains the first book I ever attempted to literally throw out a window (thankfully it failed, because I don't think it's safe for a book to fall 30+ feet potentially on to people).