While trying to narrow down why sometimes SDL takes 20-40seconds to
initialize I built up some more profiling features.
TLDR - I still don't know why SDL is taking a long time but I've
narrowed it down to it initializing the `GAME_CONTROLLER` subsystem.
This isn't unprecedented, I found numerous github issues and articles
suggesting this is the problem:

I imagine it is hardware/OS related on some level, there are even some
recent commits in SDL that have made it worse on certain platforms. I've
had this problem myself so I will hope to get it again soon so i can
debug where in the SDL code the delay occurs and make a proper bug
report. Hopefully this helps but it's not yet confirmed -
https://github.com/open-goal/jak-project/pull/3384
The current event-based approach is very difficult to get right, and it
depends on no events ever being missed. This changes the keyboard/mouse
handling code to a polling-based approach.
Other fixes:
- an issue where modifier keys were not able to be successfully bound
(like Left Shift to `X`)
- improves cursor hiding (except when you use the start menu, this seems
like an SDL issue, see comment)
- Better discarding of kb/mouse inputs when imgui intercepts input
- properly swap bindings when an already set key is assigned, even if it
crosses the distinction of an analog vs normal button
Fixes#2800