This should be easy

I was reading blogs and came across one that intrigued me. It was a supposedly challenging endgame. Having been warned, I opened up a 3 minute game against an engine and tried the first plan that came to mind (you should try that too). I expected some surprise, but instead within a minute the outcome was clear (I was actually a tad faster than the engine overall). So my question is what did I do to simplify the endgame? After all, a decent player found it challenging.
This is the blog in question (I wish to neither steal its glory, nor criticize its author who I thank for the puzzle) https://lichess.org/@/kg_wa_2024/blog/i-dont-think-this-simple-pawn-endgame-exercise-is-suitable-for-kids/NlLFLZ63
I won't bury the lead, here were my thoughts. I want to centralize the king, it's nearly always good in a king and pawn endgame. I'd quite like to swap down to have only one pawn on the board (e and d pawns could swap off), I can use my d pawn to forced him back, so success seems inevitable. As long as I keep my e pawn near the back, I don't need to worry about opposition.

1. Centralize the king.

I just shuffled my king towards the centre, e4 was the target, although I'd advance more if my opponent let me. I waste a little time keeping the opposition, when I'm going to lose it anyway. 3. Ke4 saves you a move.

2. Swap off the pawns.

Now all you need to do is trade the d pawn for the e pawn, the only issue is the king in the way.
In the game, the engine played e6. This forced you to push e3 (other moves do technically work, but it's the clearest way to advance) so that you keep the tension and pass the move. You've still got e4 so you will still be winning after the trade. The king's own pawn betrays him and forces him off the sixth rank, and once you reach e5 it's usually just technic.
As black I'd play Ke6 instead of e6. Here, you want to limit the king's squares with d5+!. You can shuffle along the 4th rank, while he only has one square on the 6th so he'll have to retreat. Kf6 is the last challenge he can offer, the idea here if that Kf5 is a second good square for the king. Reading f5 doesn't force the draw, but it's practically challenging. Kf4 stops all of his dreams.

3. Conclusion.

You can calculate endgames, and it's often even necessary. But if you apply solid principles, you might just turn a challenging position into an easy win. The game had a lot of positions where many moves were winning, but some were more winning than others.
A centralized king and a good plan can even beat Stockfish (as long as the position is already winning, and it's an endgame).
Here's how the game played out. I'm not proud of my queen mating skills.