Q.A. here,

I'm going to send this on to the team and see if we can get any ideas on this one. I can't say I've seen it before, but there it is isn't it.

In the meantime, are you able to access the settings on controller?

Also, are you running multiple displays? If so, have you tried launching it on a different display? I think I had this problem with Fallout 4 one time and that fixed it.

First launch: the right stick works as a mouse, keypad was non-functional - can't access options as the button activation boxes overlap and 'start game' gets priority.
Second launch: didn't touch the sticks, used only keypad. Technically, I could access the options now (but the controls were weird - starting from 'start game', pressing down does nothing, right jumps to credits, up goes to options, then right again to go up to 'start game').

After clicking the A button precisely 84 times, I was able to go up to my monitor's native setting (for some reason, the game launched in the worst possible entry, 3895x278 (20), and I am not sure where it got those numbers from).

Yes, dual monitor setup. Didn't see a way to launch it on any specific monitor, as it auto-launches on the main one set via windows settings. At least it did before I fixed the resolution, now it launches on the secondary one...
But what did help, was shift+win in fullscreen mode - so if someone doesn't have a controller (but has n > 1 monitors), they could do that.

Oh nice! We have a tester with an ultrawide monitor and they never encountered the issue, so I really appreciate that you found a solution. Feel free to mark that as resolved for anyone else who encounters this as well!