As it's not obvious, what is the difference between this and the current camera speed options? is it meant to enable fixing things like #4261?

This is not related to the camera stick at all. This affects left stick sensitivity allowing, for example, to set a modifier for easy ESS position or walking, both features which are not possible to perform on keyboard with current options.

It could also be useful for controller players to have a modifier set to use as a fine-aim mode.
Another consideration I'm having is to include the option for axis independent mods which would facilitate certain angle-precise tricks (enter jabu as adult with chus being a notable example) but I'm unsure if this would start to look like option bloat.

I'm not gonna lie, apart from the fact this code probably doesn't belong here but deeper down (as bria has pointed out in discord before), I'm also having big worries for this in a racing context. It's essentially a giant cheat if you look at it outside of the keyboard use case.

Besides, for the use cases outside of ESS, I feel like an aim speed modifier or something like that feels more fitting.

I'm going to close this for now. I think a modifier for keyboard sensitivity has a place but I don't think that place is here. The more I think about it the harder I see this have a proper place with racing in mind either.