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...)

Common: Replace Result with std::expected.

This fixes a build error when `-DENABLE_TESTS=ON` and `-DUSE_RETRO_ACHIEVEMENTS=OFF` are both set together, since AchievementManager is also behind an ifdef.

RetroAchievements: Updated PatchAllowlistTest to generate new allowlist

Refactors the PatchAllowlistTest to streamline the experience for developers. Instead of a textual description of what needs to change in ApprovedInis.json for RetroAchievements compatibility, the test will now generate a replacement file and instruct the coder where to copy it in their local branch, and what to update APPROVED_LIST_HASH to. The result should be easier and more instructive for developers to make changes, while still maintaining that allowed codes cannot be added or modified without recompiling Dolphin.

As ApprovedInis.json no longer needs to be user-readable for this process, it no longer contains titles or pretty formatting and as such is updated in this commit, hash included.