In this situation, as a defender needing a draw, you just need to ask yourself: "Can I keep the pawns doubled?" Or, as an attacker trying to win,: "Can I undouble my pawns?" The "yes" answer will mean you should be able to succeed in the respective task.
To be frank, I was a little surprised that this was a draw per the computer from move one all the way through to your stalemate. You did not make a mistake. My initial thought was to play the black king to g8-f8-e7, but the problem is that white can keep the K out of e7 with his own king, or keep you on the back rank, or force you to make pawn moves that are ...
What endgame principles are there/exist that would help?
You need to learn to recognise which pawn formations allow you to force a passed pawn and which don't.
The pawn formation on the kingside is almost identical to the queenside pawn formation in the Berlin Defence which is known to be unable to force a passed pawn. No passed pawn = no win.
I had an extra pawn and was closer to my pawns then White
It seems you simply overestimated these two factors.
An extra pawn alone is not a decisive advantage, it matters a lot where it is located. If the f7 pawn was on a7, you'd win.
The kings are actually positioned to your disadvantage, White's is nicely centralized and yours is stuck in the corner. ...