UI: Rename input profile

[rtavarez98]

Description of Changes

Adds feature to change a controller input profile and automatically updates the name in all games using the profile.

Rationale behind Changes

Resolves #6507

Suggested Testing Steps

Rename an existing input profile that's assigned to at least one game and check if it's been updated in a game's settings.

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[Mrlinkwii]

A very small thing , can the commit have the prefix of UI:

[Mrlinkwii]

seems to working good here on linux , its seems the Mac ci has failed @rtavarez98

[TheLastRar]

Mac CI fails with;

../../pcsx2-qt/Settings/ControllerSettingsWindow.cpp:204:52: error: no member named 'recursive_directory_iterator' in namespace 'std::filesystem'
        for (const auto& game_settings : std::filesystem::recursive_directory_iterator(game_settings_dir))

So you are missing the <filesystem> include
I don't think we use std:;filesystem anywhere else, and I would like additional testing on windows with unicode paths.

To better match existing PCSX2 code, I would suggest you instead opt for using our own FileSystem functions (in common/FileSystem.h). We have the following function which I think will suit your needs;
FindFiles(const char* path, const char* pattern, u32 flags, FindResultsArray* results)