What is the plan in this position?

Here it felt like I had the advantage due to having more space, and indeed the engine says -2.4, but the position ended up closing and we agreed to a draw.

Instead of 15... Nxf4?!, the engine prefers Nh4, but I'm not sure what to actually do after that. The engine line for the next few moves shuffles pieces around; it looks like it wants to put a knight on c4, but doesn't even end up doing that.

At what point would Black be ready for a breakthrough?

"I had the advantage"

• Yes, this is a winning position. Bd2 is like a big pawn. Bc2 stares onto pawns a4 and e4.

"more space"

• Space is overrated. You never win because of space. Chess is not Go.

15...Nxf4 is OK, the position is still winning. The problem with 15...Nxf4 is that white can make his bishop Be3 active with f5.

19...Nh6? is a mistake as it allows white to disentangle with 20 Qd2 and 21 O-O-O.

21...Nxe3? seems a mistake: why trade the knight for the big pawn on e3? Better 21...Nh4 attacking pawn g2.

17...Bd7? seems a mistake: necessary 17...g6 to prevent f5

25...Qe7 is uninspired: more active 25...Bg4 activating your bishop and bringing Ra8 into play. He can now advance h5 preventing your own ...h5.

27...f5 hinders your own play. Better 27...Qd7 and 28...h5. Your queen can then invade the weakened light squares.

28...h5? throws away all advantage. 27...Qd7 and 28...h5 was the right plan. Now with 27...f5 and 28...h5 you have no prospects.

Perhaps this (~2020) comment (by GM Kaufman) would be of interest:
"... In a general sense, what I think has changed the most is a greater appreciation of space. ... I think this is primarily a result of the engines loving space. ... the old view was that space is only important when most of the pieces remain on the board, since a shortage of space means that the pieces will get in each other’s way. While that remains true, the engines generally insist that space matters even with fewer pieces, perhaps because more advanced pawns are simply closer to queening. ..."
https://www.newinchess.com/media/wysiwyg/product_pdf/9092.pdf

Thanks for the advice. To be honest, I still would struggle to win after 27...Qd7 and 28...h5. It seems like Black is still holding it together. But I'll think on it some more.

You have space advantage, you don't want to trade pieces without strong reasons.

q2 is obviously tactcal and positional weakness.

but main thing which will contribute a lot to your chess is damn simple but very powerful....

Always check all pawn breaks in the position. So f4,q4 and c5 ( must train to see c5 too, it's important)

Objectively it's f4.

f3, c4 from opponent's side is nice if you notice too...

Wowow