h3+g4, usually prepared by Kh1 and Rg1 is a very common idea in these sorts of positions. It's one of white's main ways to get play against the Stonewall.
(Not talking about the exact position, just the general structure)
Yeah, g5 is a serious move. If black can play Nd7 + g5 to get rid of the dark square bishop he'll be doing very well. I'm surprised the OP doesn't consider this.
I've seen similar ideas (as mentioned), but the h3 move wasn't intuitive to me here because of it weakening my castled King and similarly why I didn't calculate for ...Nd7 with ...g5. It wasn't even on my radar because I judged ...g5 as too weakening of their King and giving me extra targets and ideas to play against.
I'm familiar with many Dutch Defense and King's Indian Defense game examples of black advancing their kingside pawns in front of their castled King, but perhaps I just didn't expect that out of this particular opening (and position) here.
h3 here is good, very similar to the quiet move h3 in some Queen's Gambit Exchange variation Carlsbad games (with 4 cxd5 exd5 played). In your position, White takes control of g4, so a Black piece can't land there, and secures a possible retreat for the Bf4, as well as making the undermining thrust possible, g2-g4 after some preparation. The exact same idea (taking control of g4, but in this system, to deny the Bishop on c8 any decent squares) is sometimes played in the aforementioned QGD exchange variation after White has placed a knight on e5 and then secured it with f2-f4 and sometimes following up with g2-g4 later after preparation. (this may have been known as the "Pillsbury" attack or something. Won some nice kingside attack lines with this kind of system.
Your post resonated with me because I play the QG Carlsbad structures often and I like your explanation regarding the e5 Knight and following plan. I've had this come up in a few of my games, but in practice, I usually get h3 and little else moving on the kingside (f4 and g4 etc.) as I'm usually playing for the center f3-e4 pawn break, or playing thematic ideas on the queenside (based on the exact position).
Thanks for sharing your knowledge. I liked your QG exchange example.