I will start by stating that all positions with the rooks traded and Black's pawn traded for any of Whites pawns is drawn. You can explore this for yourself in the 7-man tablebase.
We can use this information to understand that Blacks main defensive technique is to threaten the trade of rooks. This narrows the initial variation to 1...Bc6 2.Kf2 as only Kf2 properly deals with the threat of Ra2. Now after 2...Kf5 White again has an only move to avoid an obviously drawn situation: 3.Re2.
After these more or less forced moves we reach the critical position.
[FEN "8/8/2b3p1/4Bk2/r4P2/8/4RKPP/8 w - - 0 3"]
As for if this is a draw, Black already has the option to play 3...g5 forcing a trade of pawns. With all the pieces active and an opposite colour bishop dynamic I would put Black as a big favourite to draw.
Stockfish 13 prefers to delay g6-g5 for a few more moves, starting with 3...Bb5 and gives an evaluation of 0.94 at depth 45.
With either third move from Black the position should be a draw as White cannot make progress due to the constant harassment from the rook and bishop, combined with the Black king standing firmly in front of the pawns.