Happy about Converting Rook Endgame

So, the rest of this endgame was pretty spaghetti, I was able to get something close to a Lucena position, but then I flubbed around for a bit. Nerves, plus I just don't have a lot of practice in rook endgames yet.

But I have at least been trying to understand them. And the position eventually simplified even further. I think normally, I would have just flubbed this endgame too and agreed to a draw. But I'd been trying to string together a couple ideas that I was half-remembering from Jesus de la Villa's 100 Endgames. Anyway, here's the conversion. Apparently, Rd4+, keeping an eye on the h4-pawn, also wins, because black's king can never move away from guarding h4, but that's not the idea I saw in game. Just happy about this, because this is something I absolutely would have blundered two months ago.

Good job man, what was the time control for this? Also I'm guessing black resigned here? It says 1/2-1/2 but I think it was actually a win for you.