Hotkeys: New Input profile swapping hotkey(s)

[Tundrak]

Description of Changes

Hotkeys: New Input profile swapping hotkey(s)

Two new Hotkeys to cycle the Input profile for a specific game forwards and backwards alphabetically between the Shared input profile and any custom ones. They are contained in a new section called "Input".
Changes get saved in the game settings INI file, so they persist after shutdown and don't override global Shared settings
When the hotkeys are used a notification is displayed with the name of the new Input profile

Rationale behind Changes

Giving a way for users to rapidly change their Input profile without leaving the game window. This helps in games with sections/modes where the commands change wildly and might become uncomfortable to play with the same profile.
Closes #7325

• Note: While researching I found this page in the documentation which says this pull request shouldn't really be allowed, but then the Issue I mentioned was accepted so I guess this is fine...? Feel free to close this if it wasn't allowed

Suggested Testing Steps

Assign a binding to the hotkeys from the Settings menu and then test them on any game (or the Padtest ELF) with any number of Input profiles created

• There is currently a bug where switching Input profiles while pressing any button makes that button get stuck in the pressed position until you press it again with the new binding. I tried various methods to get it unstuck but couldn't find anything working. I also see this is a problem already occurring in input recordings (see [BUG]: Buttons getting stuck when stopping input recording playback #13235). Maybe someone could suggest a solution?

Did you use AI to help find, test, or implement this issue or feature?

No

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[Tundrak]

Fixed an error that prevented Linux builds from passing, this time I tested them on my fork and they all complete