I know it's standard to use Wesley to illustrate the term but I don't believe it works, not once you start to break it down.
A Gary Stu represents wish fulfillment on the part of the creator and what that means in any given case will vary depending on the specifics.It makes no sense to refer to a character as such if we don't look at the wishes they are supposed to be fulfilling. My Gary Stu is likely quite different to yours. Yes both would be insanely competent and idealised versions of ourselves, but crucially they would be extremely competent and idealised versions of ourselves as we wish to see it.
If we had any sense of Gene Roddenberry having a yearning for technical genius or socially awkward prodicy I'd be inclined to agree but the truth is at the time of TNG he was in a totally different place mentally.
GR at that point saw himself as a humanist, an inspiration and a social visionary. That was how he had been lauded since the 70s and it had become his go to reference for his narcissism (and he was extremely narcissistic). Whether those terms could correctly be used to describe him is another matter, but they certainly don't apply to Wesley Crusher. If GR were to have taken his internalised self perception and put it on screen it would probably look something much more like Picard or the latter day Spock.
Going further back to TOS and we have a totally different person in many respects, one much younger and for whom "wish fulfillment" would look more like the ambitious, uber masculine, charismatic and promiscuous James T Kirk.
A much smaller part that springs to mind would be Gorkon if he'd been around to play a part in TUC.