Thinking only nanoseconds about the question my first thought is this: after 22.Rd2 (page 111 of the book) we write: "Rd2 blocks the King's principal path of g1-f1-e1-d2-c3. Moreover it leaves the 'b' file at Black's disposal: 22...Rb8 23.Rc1 Rb4 with counterplay".
The whole idea of delaying moving the Rf8 and playing first g6-Kg7 is that we don't know where this Rook belongs, so we imporve first the position of the King. So, after
22.Rc1 g6 23.Rd2 (your question) Black has the opportunity to play
23...Rb8. Am i correct? If
24.Bf1 Rb4 25.Rdc2 Ra4 26.Bxc4 Bx 27.Rx Rxa2 Black's King is close enough (Kg7-Kf6) to sequre a fairly easy draw. Another variation which is simple enough is
25...c5 26.Bxc4 cxd4 27.Bxe6 Rxc2 28.Bxf7+ Kxf7 29.fxe3 Ke6, according to Marin's algorithm (see first chapter of Learn from the Legends) Black should be able to draw easily here because he has only a "-1" (minus one) score, or the score is even "-0" because he has the more active King and the more active Rook (who can swing to the 'a' file soon).
If this doesn't seem appealing because we are playing only for a draw (and i can understand this, but for some others sequring a fairly easy draw is more appealing!) i would think of playing 23...Rd8 first (because we need now to play ...c5 after Bf1) and improve first our King because we want to avoid the above variation where the Bishop takes on f7 with check. This is one important detail in the position! That's why we say that we "improve" our King by putting it to g7. So,
23...Rd8 24.Kf1 Kg7 25.Ke1 Kf6! (instead of your ...a5 or ...Bd5) and if
26.Bf1 c5! when i am sure that Black is comfortable. Or
26.Kd1 Rb8! when we have a much more improved variation of the 23...Rb8 line because my King has improved while your King's improvement is not as obvious. Of course i could play
25...Rb8!? but i think that ...Kf6 is a bit more usefull than White's Kd1, so before i play the ...Rb8 idea i want to get the maximum of my position. Black certainly can play here for a bit more than a draw if he gets at the 'b' file, even if it is still level.
Again i am answering this question only by instict, which is extremely well developed by analysing this endgame for months! (I am sorry if i blundered somewhere. A more responsible author would check first his line with an engine!) I am reminded now of Tiger's chapter from
Grandmaster vs Amateur where he expresses the opinion that the amateur can close the gap if he specialises in certain positions and gets the opportunity to play those positions against a Grandmaster. After spending hours and hours analysing this endgame imagine my pride when i was playing matches against Houdini or Rybka and never (or almost never to he honest) losing! OK, computers may be not the best in these technical positions where they go to endgames which are easily drawn (for example 3 vs 2 Rook endgames) but they still believe that they hold an edge, but anyway it is a nice feeling and i recommend you doing the same after studying this endgame seriously. Then if that appears on the board in a game of yours we'll be armed with great confidence and experience to play it. In a practical game this matters much more than the objective evaluation of the position (and in our case several Grandmaster we have asked confirmed that this endgame is drawn by best play).
Really thanks for an interesting question!