Football

I think you've about nailed it, it's a bit harsh and takes away from the good mood of actually winning a tough game we might have lost rather than swanning around thinking we'll do alright and fucking up.

If Southgate has done something he's done this:
He's worked on his image, how he wants to talk, how he wants to be seen.
He's worked on the way he presents himself to his staff
He's worked with his staff to be inclusive
He's worked with his staff to develop a new, fairly positive, mood within the England set up
He's worked hard to say "no, this is the way we're going to play, this is the way we're doing things". It appears to be connected all the way back to the academies.
He appears to have bypassed the shit tabloids
He's cleaned out a lot of shit (Wayne, Joe et al)
He's got the team playing in a consistent manner, they don't panic (yet).
They're not inspiring, they did look tired after the first half, they will be shell shocked (they're young, they've not been exposed to regular high level football (perhaps?)).
He's broken the reliance on "plays for a top 4 team, has experienced european big cup" (which i've banged on about in here as being the previous managers' criteria for selection (before "are they good?" and "will they gel together")).

More than anything else, and he can get us knocked out by Sweden for all I care because of this, he's got a team through a fucking penalty shootout. How much of it is down to the "owning the process" and how much is luck (henderson, dier, the missed Colombian penno) I DON'T CARE. That is one less thing to think about as an England footballer.
Also, that's the first win in a knockout game since when?

tl;dr
he's performed some sort of augean stable clean
he's connected the team to the england youth set ups
he's broken the hoodoo around pennos

I've seen knighthoods given for less.