Accomplished using `run-clang-tidy` with `performance-move-const-arg,performance-unnecessary-value-param,modernize-pass-by-value`.

Changed arguments to const references, removed them where inappropriate (e.g. sink parameters). Same with std::move.

Manually reviewed each change to make sure that it makes sense, and do something more appropriate if possible.

Remove unused vector `controller_names` from `LoadConfig` and
`SaveConfig`. The vector has names added to it but they're never used.

Prior to d03f9032c129e440e4f07d319be8b52500798e07 these vectors were
passed to `DynamicInputTextureManager::GenerateTextures`, but that
commit removed those calls.

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...)

Because the last commit made us use separate folders for GCPad and
GCKey profiles, we should also use separate game INI keys for them.
Otherwise setting e.g. PadProfile1 in a game INI will make both GCPad
and GCKey try to load it, typically with one of them succeeding and the
other one showing a panic alert due to the profile not existing in its
folder.

Better do this breaking change for GCKeys in the same PR as the other
breaking change rather than later.

After reading the previous commit, you might think "hold on, what's the
difference between GetProfileName and GetProfileDirectoryName"? These
two are being used for the exact same thing - figuring out where
profiles are stored - yet they return different values for certain
controllers like GC keyboards! As far as I can tell, the existing code
has been broken for GC keyboards since they were introduced a decade
ago. The GUI (and more recently, also InputCycler) would write and read
profiles in one location, and our code for loading profiles specified in
a game INI file would read profiles in another location.

This commit gets rid of the set of values used by the game INI code in
favor of the other set. This does breaking existing setups where a
GCKey profile has been configured in a game INI, but I think the number
of working such setups is vanishingly small. The alternative would make
existing GCKey profiles go missing from the profile dropdown in the GUI,
which I think would be more disruptive. The alternative would also force
new GCKey profiles into the same directory as GCPad profiles.

This commit also fixes a regression from d6c0f8e749. The Android GUI was
using GetProfileName to figure out what key to use in the game INI,
which made it use incorrect game INI entries for GameCube controller
profiles but not Wii Remote profiles. Now the Android GUI uses
GetProfileKey for this, fixing the problem.

By having getters for this information, other code that needs access to
the same information can call the getters instead of duplicating the
information.

This only matters for analytics, but still.