Making a better move after analysis

Three hours ago I played 9.e5?! after my opponent's 8...d4?! (I had the feeling that black could not play so sharp in this position and that the d pawn push was not correct). However, analysis after the game with Lichess Stockfish showed that white can take on d4 first. Did so in the second game below.

And I had to chance to test that just now (Game : 0/0/0, 11 acpl).
I'm sharing my thoughts during the game, also about the resulting rook endgame (I'm quite a rook endgame fan btw)

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