A stalemate puzzle

The recent Dublin Blitz Championship 2020 (Gonzaga College, February 2) featured a game in which one player had the misfortune to resign in a position where he could force an almost immediate draw by stalemate. Well, these things happen: it’s not always easy to see everything on an increment of two seconds per move.

But there is an interesting puzzle buried within the game, regarding the diagrammed position:

O’Cuilleanain – Przyborski, Dublin Blitz 2020
6… ?

The game went 6… Ra4 7. Rc8, and now Black could have played the obvious enough 7… Rxa6+, since 8. Kxa6 is stalemate.

But if Black instead played 6… Rb5+!? in the diagrammed position, what would happen with best play? Does Black have a draw, or can White escape?

I freely admit I got this one wrong, even with much more than two seconds to think about it.

[Click to replay game (including solution)].

(See also the YouTube video of the finish.)