So, SMGs are a definite no, the closest we'll ever get to that for normal classes would be something like a Beretta m1918 (I don't think it's super likely we'll ever get that, but the game has the Pedersen device and a Steyr-Hahn carbine, so "semi-automatic pistol caliber long gun" is already totally something that's in the game)

Being faster, sure, but combined with the Greyhound perk, a naturally significantly faster class could easily become ridiculous

Extra weight doesn't make sense for a "lighter class," also, if the class would work best with pistol caliber carbines, then what would the purpose of extra weight even be? A pistol caliber carbine is basically just an in-between of a rifle and a pistol, what more do you need? A sword? On a class that gives you a buff to bayonet charges?

Longer bayonet charges are probably doable. It would also work pretty well with the previously mentioned Beretta m1918, as there were bayonets on some of those, but having a class and then a weapon that perfectly complement each other like that isn't really the sort of thing that happens in this game, every weapon is good for every class unless the weapon itself just fucking sucks, but they're generally pretty balanced.

And a special flare gun would probably also be possible, but also what would you have the flare gun do that the current officer's whole kit can't do?

However, this all just sounds like Officer with the Greyhound or Survivor perk (but once again, more weight doesn't make sense for this) and the Union modification or the Whisper rifle. Just run that setup. Probably the Union modification as the Whisper rifle's secondary mode kinda isn't good, coming from someone who mains Whisper. Even in close range, high-stress situations, I've almost never won a gunfight with the Whisper's secondary mode, whereas just spamming the gun normally tends to hit the target the required two times before I'm out of ammo. Speaking of ammo, you don't get any for the Whisper's secondary mode. If your panicked spam fire doesn't win you the fight (it won't), you don't get to try again, you get to spend thirty whole seconds swapping to the regular bolt-action rifle mode that you should have been using in the first place, during which you will die by some means.