Thanks to the input of my readers, I start to make sense of this position.
I played it a few times with white (hattip Aox) and with black against a somewhat restricted engine (20 sec/move, hattip mr.Z). After just 3 attemps with black I already managed to win this position against the computer. I will try it with an unrestricted engine later.
I will give a summary what I found sofar.
Let's first paint a picture of the statics of the position.
If you think away all the heavy and light pieces, there probably remains a won pawnending for black.
If black plays e4 and f5 he has a protected passer, meaning that the white king cannot leave the square of the e4 pawn. Black must enter the square of a4 timely of course, but then he can take his time to get rid of c5 and a4. Thus creating a second passer. The win is then easy. If blacks king is not in time, white can create a passer that can't be stopped while blacks passer will be stopped by the white king.
If we add the bisshops to the pawn ending, the outcome will probably be the same. If we add a rook in stead, one plus pawn is probably not enough to win. As Soapstone pointed out.
So blacks goal is clear: trying to exchange the queens and the rooks, getting a protected pawn on e4 and get rid of a4 and c5.
Let's take a look at the dynamics of the position. The white king isn't quite save. He must be aware of backrank threats and of pressure against g2. White has more space and a majority on the queenside which might become a weapon in it's own right.
The black king isn't quite safe either. If he leaves the back rank with his rook, his bishop might become vulnerable when a heavy piece of white reaches the 8th rank.
The black bishop must keep an eye on the black squares around the king, so he can't be used for attack solely.
Further he must be aware of pressure against f7 over the f line and the
diagonal a2-f7. In fact that is the reason that the queen and rook e6
are standing where they are.
As long as the queens are on the board, f7 is commited to its place and cannot help the e-pawn.
The pawn on b7 is weak.
Attack or defense.
Black wants to trade the heavy pieces. He can do so in two ways. When black focuses on the defense, his lack of space causes him trouble. He will probably manage to trade the heavy pieces. But not on his own conditions. And that is what happened in the game. I traded the queens because I needed to get rid of the pressure, but it gave white the chance to connect his pawns. The lack of space for defense leads to another risk: the chance to loose b7 without compensation.
The right way to force the trade of pieces is to attack (hattip mr. Z). Attack forces white to defend. Defense immobilizes the pieces. Immobilized pieces can be traded. But now on the terms of the attacker. e4 is a move that creates space, leads to an outpost on d3, thus giving chances for trade.
I was hesitant to play e4. It releases the black diagonals, and since the black bishop has more defensive duties than the white bishop, probably white's bishop is going to profit from those diagonals. What I underestimated is that the white bishop has duties too: keeping an eye on e3 and c5.
Further I underestimated how bad idea it is to try to defend yourself under the conditions of lack of space.
Qc6 in itself is not such bad move. What is bad about it is that there is no plan behind it. There were some vague ideas about pressure against g2 and a4, but nothing that is going to materialize anytime soon.
When I got such positions in the past, I used to be in time trouble all the time. When I was ahead, a draw offer of mine was often accepted. When not, I usually lost in time trouble anyway. When I was equal or behind, I usually lost it too.
So I never had the chance to get some exercise in these positions. But now I reach these positions with still an hour on the clock, it is time to learn to play them. Avoiding them by offering a draw is no longer an acceptable option, since that deprives me from the chance to learn something.
Thanks to the valued contributions of my dear readers, I finally get some insight in how to play these kind of positions. Thank you all for that! It has been very clarifying.
I simply must make a plan based on the statics and the dynamics of the position, and I must value an active approach much higher than a defensive approach, just in order to force the necessary exchanges on my own terms. The endgame exercises prepare me for the static evaluation of the position. But I must learn to evaluate the dynamics by feedback from practice.
20 hours ago