Oh boy, that game hurts me, I think Im gonna stay away from the internet after posting such a trash played by me, lol
So far, if we dont take in account how I reached that position I think I can try and be Magnus.
Right now I am looking at 22...Nd6 23.Bf4 with the idea of getting rid of that knight if allowed and then push with g4 (early g4 = hxg4-fxg4 and now e4 is horrible).
A sample line may be the following:



White looks a little bit better and with my nonexistent endgame technique Im hoping to outplay Stockfish in this endgame

I know that this is correspondence chess, but I have to say that if this should be busting or unbusting this line, then I have to rethink everything I know about chess. 14. Nxc6 and then the following moves from both sides look completely illogical to me at first side. The way both sides give up their e-pawns....I just don't get it, I'm sorry. And then letting Bxc3 happen, I do not understand anything of that. Maybe I'm just an idiot though.

What about this following line with Rab8? I am right now playing it on a unrated correspondence chess with a guy that thinks Qa5 is not refuted. I thought the opposite but had too many games ongoing and couldnt find anything better for this game.
I thought it would be easy to beat him because it looks like he only turns on Stockfish and sits him there for 2 days, but who knows, I ended up doing almost the same cause I had no time to think (too many damn games)



I still think the Dragon is busted and I dont think there are many improvements before Kb1, Nxc6 was suspicious and I didnt want to play that thing, but couldnt find anything better with the little time I had.
Perhaps my opponent just unrefuted the Qa5 lines?

Incidentally, that h4 + Kb1 + Nb3 was considered quite strong about 45 years ago (in "The Sicilian Dragon" by David Levy).

Here is the correspondence refutation I think. It comes from a game on the ICCF. The game there was drawn tho, so I dont know if the engine correctly evluates the endgame by saying White is almost winning +0.90 or is it a draw.


The other move in this rather long sequence is 19...Nxd6 but I think that gives White way better play as he can simply play c3 followed by a Qf2-Bc5-Rhe1 to pressure e5. White reaches a nice position where Black has no attack and White is solid/winning.



Black's other try that hasnt been refuted as hard as Rfc8 (at least in the ICCF where White wins like 99% percent of the games) as I could only find 2 games from the 2004-2015 ICCF archives. However I think it is also busted.



That right there is a weird Soltis and I think both 13.Kb1 and g4 are good responses. Here is a line I think kind of refutes it, however I havent had a serious, strong black player take a look at this lines (most of them dont waste time on Qa5 but instead on Topalovs or the exchange sac lines with b5-b4).



The most common move is 14...Kf8 which is weird as hell, at least for a Dragon middlegame, however I havent done serious analysis on it.

This thread reminded me of another queen move from the 1960s:  to b8.

After the standard moves 1.e4 c5 2.Nf3 d6 3.d4 cd4 4.Nd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.f3 0-0 8.Qd2 Nc6 9.Bc4 Bd7 10.0-0-0 Qa5 11.Bb3 Rfc8

AFAIK, the line that Bragesjo gave is currently considered the most challenging for Black and perhaps an actual refutation.  12.h4 Ne5 13.Kb1 Nc4 14.Bxc4 Rxc4 15.Nb3 Qc7 16.g4 Rc8 17.e5! +/-. 

In this line, Black can deviate with 13...b5 instead, but he does not reach full compensation for the pawn after 14.Ncxb5!  Still, this may be Black's best try.  On the main site, a few years back, GM Ward analyzed one of the critical positions out to a point where he concluded that White kept an edge, but Black still had play.

There may be other problems too.  Andy Martin once gave 12.Kb1 Ne5 13.Bg5 as another refutation. Ree-Tal, 1973, continued: 13...Nc4 14.Bxc4 Rxc4 15.Nb3 Qe5 16.Rhe1 Rxc3 17.bxc3 Be6 18.Be3 Rac8 19.Bd4 Qb5 20.Ka1 Qa4 21.Rb1 Bf8 and now Ree could have played 22.Bxf6! exf6 23.g4 with advantage.

Even in the old main line where White avoids Kb1, it isn't clear that Black can equalize.  12.h4 Ne5 13.g4 b5 14.h5 and now 14..b4 was Nunn's suggested improvement on his game vs. Ward, 4NCL, 1998.  Both Nunn and later Dearing, in his book, analyzed this to a position that they evaluated as unclear, but today the engines think White is better in this line.

Your suggestion looks like a mixture of two systems (Qa5 and Soltis) which don't fit very well.
Normally black never plays h5 in these systems, after moving the rook away from f8 the pawns on white squares are now especially vulnerable (e.g. f7).

Either way I prefer a white system with Kb1 and Bg5 instead of h4, but as others said this is not the only way to set black problems.
The Qa5 variation has seen its best days long ago, now there are some more promising systems in the Dragon (Topalov System, Chinese Dragon).