Avoids unwanted implicit conversions. Thankfully, given the large amount
of cleanup in past PRs, only this tiny amount is left over to cover.

This makes clang-format useful on those.

Also add a bunch of forgotten transitive includes, which otherwise
prevented compilation.

This is exposed in the GUI as a new "CiTrace Recording" widget.

Playback is implemented by a standalone 3DS homebrew application (which only runs reliably within Citra currently; on an actual 3DS it will often crash still).