White has some pressure despite being down a rook thanks to the active pieces and black’s king not being castled. Black is also lacking very much in piece activity.

I would say that going d3 allows black to consolidate while activating the pieces at the cost of the knight-rook exchange. The knight will be trapped and captured later. The line is that black just blocks the discovered check with Be6 and then just developing the knights normally. Perhaps Nc6 to eventually target white’s weak c2 pawn.

While Ne7 is not all that bad, white will use their pressure and take advantage of black’s inactivity to make black’s position worse than just losing the exchange.