No I am not saying the berlin is bad :). Though at top level, true it is being played quite often, at lower levels like 2500> the closed is very often. Actually recently a 2600 played the main line with Na5 c5 etc
no sacrfice time
Still curious about ..Nf5 versus ..Ne4 on move 12. The top players prefer the latter, but the knight move to f5 is very natural. It's a pretty unique case where it is better on e4, but I don't quite know why.
Maybe 12...Nf5 is playable, but 13...d5 is certainly wrong. Bb7 is dead wood then. Black realised this when he retreated Bc8, but that means that ...b6 and Bb7 and Bc8 are 3 lost tempi or about a pawn, roughly enough to lose. Without 13...d5 e.g. 13...Re8, then what is the knight doing on f5? On e4 the knight is so much stronger. I think it is either ...b6 or ...Nf5. ...Nf5 gives the same position with 3 tempi gained as compared to the delayed 12...Nf5.
I completely agree about 13.d5 being wrong. It's a routine move that one should not make after putting the bishop on b7, even though it is the most natural move in the world in this structure.
12..Nf5 is definitely fine, but 12.. Ne4 does seem to be more precise. I think that the reasoning is that Black wants to trade the knights when White goes ..Nd2, which is hard to avoid for him. The Motylev-Giri game in the line ends in a draw after only a short 18 moves, but I think that Motylev had room to play for an advantage there. Especially deviating on move 16...
I still doubt 12...Nf5. The main trait of this position is the open e-file. That makes the outposts e5 for white and e4 for black ideal squares to put a knight on.
There are two ways to put a knight on e4.
...Nf5, ...d5, ...Nd6, ...Ne4
or ...b6, ...Bb7, Ne4
The second is more efficient: one move less and also the bishop is developed and the rooks are connected to contest the e-file. Also the pawn still on d7 can chase a white knight out of e5 if needed, impossible after ...d5.
A knight on e4 is the best way to force a trade of Knights: white cannot let it stand there on that strong position. Otherwise white must chase it with the weakening pawn move f3.
I do think that the main idea of ...Ne4 is to trade that knight for the b1-knight as soon as it lands on d2.
Nf5 ends up being awkward, because if you don't follow it up with ...d7-d5 then why did you put it on f5? And of course d7-d5 no longer makes any sense with the bishop on b7, so we arrive at the conclusion that the knight must be better placed on e4. Besides, as you pointed out, it is just a good outpost square, and is one of the main advantages of the bishop being on b7 as opposed to the main lines.
Of course the idea of …Ne4 is not to capture ...Nxd2, bur rather let white capture Nxe4 and the recapture with Bb7 or d5 or Re8.
Occupying a strong point is a more efficient way to trade pieces than chasing after the trade.
If black plays ...Nf5, ...Nh4, ...Nxf3
and white replies Nbd2, useful move, Nxf3 then white has played some useful move and still has a knight on f3.
If on the contrary black plays ...Ne4, ...useful move, piece recaptures e4
and white goes Nbd2, Nxe4, useful move
then white also has his knight on f3, but black is a tempo up and still occupies the outpost e4, albeit not with a knight.
Grandmaster gave up early. I would still play in his place.