I have the Steam version but it maxes out at 2560x1440. If this one supports widescreen I'll buy it immediately.

EDIT: I was able to set the resolution with GeForce Experience and it actually used the whole screen!

But the games own menu should be updated to support widescreen resolutions...

I know the struggle. Here's your solution.
You need the mod "Ultra Wide Interface (21x9)" for the HUD
Link: https://www.nexusmods.com/fallout4/mods/65677

I also recommend "Fallout 4 Configuration Tool - By Bilago".
It's the easiest to tweak the settings for custom resolutions (see attachment).
Link: https://www.nexusmods.com/fallout4/mods/102

If done right, the main menu should be within the green square (see attachment).

Thanks!