Yellow squiggly lines begone!
Done automatically on .cpp files through `run-clang-tidy`, with manual corrections to the mistakes.
If an import is directly used, but is technically unnecessary since it's recursively imported by something else, it is *not* removed.
The tool doesn't touch .h files, so I did some of them by hand while fixing errors due to old recursive imports.
Not everything is removed, but the cleanup should be substantial enough.
Because this done on Linux, code that isn't used on it is mostly untouched.
(Hopefully no open PR is depending on these imports...)

Also update the names of the setting post-Steam Deck commits to SDL

Fixes https://bugs.dolphin-emu.org/issues/13412

This specific issue was already addressed by https://github.com/dolphin-emu/dolphin/pull/11635
though I felt like there was something more we could do, and wasn't too happy with the
likelihood of devices update calls being skipped (due to `m_devices_population_mutex` being locked).

This reads Steam Deck controls bypassing Steam Input. This allows for access to
motion controls as well as independent access to thumb sticks, trackpads, and
back grip buttons.