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Why is f3?! an inaccuracy, but g3 is correct?

This is my most recent game. I completely out sourced my opponent. It felt like I played 100% accurate. Comes to find out I had one inaccuracy?! Apparently f3?! was wrong and g3 was the right move. The understanding for me moving f3 was to keep the pawn chain rock solid and f3 also allows my knight on c3 to move to a better square and no longer having to sit back as a bad piece and protect the e4 pawn from Black's knight on f6. I am looking for any insight as to why g3 is better here.

Thank you and keep Elo Hunting!
I don't get the point of 16.g3, either. But if you wanted to free your Knight, I think 16.Bd3 was better and makes possible Ne2.

After 16.f3:

* there are no good places for your Knight to go (a4 or b1 don't look particularly appealing),
* your LSB is trapped,
* your King will be exposed (not immediately, but a few moves ahead),
* unless it relocates to h1,
* but your g3 square is now weaker than before, so think about Black playing Nh5-Ng3.

It is quite interesting that in the actual game your Na4 was indeed a winning move, because another pawn mistake by the opponent. Pawn playing is very tricky.
I don't think your knight was terribly placed, and I am not sure where I would like to have it instead, except on f5 at some point, and the route would go over g3 or probably e3.

f3 weakens the dark squares and limits the range of your light squared bishop. For example Nh5 would be my immediate reaction as black, and probably planting it on f4. If you take it, after exf4 Black gets the nice e5 square for his other knight.

Also note that your opponent has a dark squared bishop. g3 limits its range. f3 enhances its scope and makes your escape squares potentially inaccessible.
And just to add:

Those moves are always easy to rationalize in hindsight with the engine eval next to it.

If you played g3 and the engine suggested f3 as better, I am sure we would have come up with good explanations as well... "secure the center, Black has no way to take advantage of the weakened dark squares, strong queenside attack coming, blablabla".

Chess is difficult, especially during the actual game. :-)
I thought g3? why not a3 then I turned sf on and indeed first it chooses g3 later a3 but at equal eval. f3 does seem like a logical move too but maybe that is trough human eyes
quite simple , f3 blocks youw white bishop while it needs more space to move, besides g3 allows to push h4 paw after making nice pawn structure with opened bishops