ZDoom

One time, when I reset my whole GZDoom settings because I was switching from an old 2.0 (I think it was the latest of the 2.0 versions actually) version to the latest 4.3.1 and got new hardware, I noticed that my weapons have changed, for all games.
They feel more "up front", like I can see the metal butt of the shotgun and some hand sprites on the supershotgun.

This made me wonder, what actually made it so? Is there a command, console or otherwise, that changes "viewmodel FOV"?

There is the "fov" console command, but I doubt that's got anything to do with it. Something in the source code that got changed with the implementation of ZScript is my best guess.

All I can think of right now is the Weapon.YAdjust property in Decorate & ZScript. Positive values shift the sprite down, negative raise it. Heretic's crossbow has a YAdjust of 15 for example.

did you switch from statusbar to fullscreen hud?
the statusbar hides a little of the lower part of weapon sprites