My Stockfish disagrees with your Stockfish. It's still grinding but the jig is up. The issue is that Black's Bishop and Rook are pinned down and defensive and White has a passed e-pawn that can be supported on the 6th rank.
Also, Black is nearly in Zugzwang.
[FEN "5k2/p5pp/r7/2pB2p1/b1P5/6P1/4PP1P/R5K1 w - - 0 1"]
1.Ra2 g4 (1... Bb5? 2. cxb5 Rxa2 3. Bxa2) 2.h3 h5 3.e4 Ke7 4.e5 Kf8 5.hxg4 hxg4 6.Kf1 Ke7 7.Ke1 g6 8.Kd2 g5 9.Ke3 Kf8 10.Kd3 Kg7 11.Bb7 Rb6 12.Bc8 Rb4 13.Ke4 Rxc4+ 14.Kf5 a6
Yeah, these moves are very robotic. Black's g4 is about as good as it gets. Ke7 and h5 are much worse for Black than g4.
So, why Ra2? After 1 ... Bb5, white has 2. bxb5 and the White's bishop defends the rook. So sneaky.
EDIT - I let the computer play the game out, 5 minutes per move. It would not be easy to win this. What I am seeing is that the initial analysis is generally good, but Stockfish gains a lot of clarity by playing it out. We see that White's second move differs from the analysis above.
[FEN "5k2/p5pp/r7/2pB2p1/b1P5/6P1/4PP1P/R5K1 w - - 0 1"]
1.Ra2 g4 2.f3 gxf3 3.exf3 Ke7 4.h4 h6 5.Kf2 Kd6 6.Ke3 Ke5 7.f4+ Kf5 8.Kf2 g5 9.fxg5 hxg5 10.Bb7 Rb6 (10... Ra5? 11.Bc8+ Kf6 12.hxg5+ Kxg5 13.Bd7 Ra6 14.Rxa4 {and now black pays the price for allowing the pin}) 11.Bc8+ Ke4 12.Rxa4 Rb2+ 13.Kg1 gxh4 14.gxh4 Rb8 15.Be6 Rh8 16.Bd5+ Kd3 17.Kf2 Rxh4 18.Rxa7 Kd4 19.Kg3 Rh8 20.Kf4 Rh6 21.Rd7 Rh4+ 22.Kg5 Rh2 23.Bf7+ Ke4 24.Rd5 Rh8 25.Be6 Ra8 26.Rxc5 Rf8 27.Rd5 Ra8 {And now Stockfish announces a mate in 20+ moves, or something, lol}