?? Or !! Or Something In-Between?

MY round-three game from the weekend's Hampstead U2200.
Spanton (1840/170) - Julia Volovich (1662/164)
Jobava-Prié (aka Barry Attack)
 1.d4 Nf6 2.Nc3 d5 3.Bf4 e6 4.e3
The most-popular alternative is the thematic 4.Nb5!?
4...c6!?
This has been played by Russian grandmaster Valentina Gunina, but seems slow.
5.Bd3 Bd6 6.Nf3 0-0
A critical test of White's set-up is surely 6...Bxf4, but that does not mean the text is necessarily inferior.
7.Ne5
All three games in ChessBase's 2020 Mega database saw 7.0-0.
7...Qc7 8.Qf3 h6?!
This gives White a target for a quick kingside attack.
9.g4 Nfd7!?
The choice of the analysis engines Stockfish10 and Komodo10, but it leaves Black's kingside looking awfully bare.
10.Qg3
The engines reckon 10.g5!? is even stronger, their mainline running 10...hxg5 11.Rg1 Nxe5 12.dxe5 Bxe5 13.Bxe5 Qxe5 14.Qh5 f5 15.0-0-0 with a huge attack for two pawns.
10...Bxe5

I recaptured on e5 with the d pawn. How would you annotate the move?

*****
*****
*****
*****
*****
11.dxe5!
I played the text without seeing Black's bishop-trapping reply, so in a way the move, or at least my playing it, deserves double-question marks. But the engines reckon it is White's best move in the position, which is why I have given it an exclamation mark.
11...g5 12.0-0-0?!
The best follow-up seems to be 12.Qh3, when 12...gxf4? loses to 13.Qxh6 f5 14.Qg6+ Kh8 15.Qh5+ Kg8 16.gxf5 etc. So Black has to try 12...Nxe5, but the engines continue 13.Bxe5 Qxe5 14.Qxh6 (14.Qh5!? also has its points) Qg7 15.Qh5 Nd7 16.h4 Nf6 17.Qxg5 Qxg5 18.hxg5 Nxg4 19.Ke2 with advantage for White.
12...gxf4 13.Qxf4?
White had to play 13.exf4, when the engines give 13...Kg7 14.Rhg1 with a position hard to assess - Stockfish10 has White winning, but Komodo10 reckons the position is equal if Black finds 14...Rh8!? (Stockfish10 strongly disagrees).
13...Qxe5 14.Qxh6 Qg7 15.Qh4 b5 16.Ne2 Nc5 17.Ng3 Nbd7 18.Nh5 Nxd3+ 19.Rxd3 Qg6 20.f4 Nc5?
This loses control of the f6 square, and so allows White to draw. Black is winning after, for example, 20...f6.
21.f5 Nxd3+ 22.cxd3 exf5 23.Nf6+ Kg7 24.gxf5 Bxf5 25.Nh5+ Kg8
Black offered a draw.
26.Nf6+ Kg7 27.Nh5+ Kg8 ½–½