[input] Fix mouse drift on Qt/SDL frontends (#4352)

Fixes regression from #4229

Mouse wasn't updated periodically to prevent "infinite drift".

Timer for polling is now controlled by frontend directly, this should reduce latency considerably and wasted cycles spinwaiting, it also removes an extra thread which is always welcome.

- [x] I have read and followed the [Contribution Guidelines](https://git.eden-emu.dev/eden-emu/eden/src/branch/master/CONTRIBUTING.md#code-contributions).
- [x] I have read and followed the [AI Policy](https://git.eden-emu.dev/eden-emu/eden/src/branch/master/docs/policies/AI.md)
- [x] I have read and followed the [Coding Guidelines](https://git.eden-emu.dev/eden-emu/eden/src/branch/master/docs/policies/Coding.md) to the best of my ability.

-------------------

Reviewed-on: https://git.eden-emu.dev/eden-emu/eden/pulls/4352
Reviewed-by: CamilleLaVey <camillelavey99@gmail.com>
Reviewed-by: MaranBr <maranbr@eden-emu.dev>

src/yuzu_cmd/emu_window/emu_window_sdl3.cpp

@@ -37,10 +37,16 @@ EmuWindow_SDL3::EmuWindow_SDL3(InputCommon::InputSubsystem* input_subsystem_, Co
         SDL_SetWindowTitle(this_->render_window, title.c_str());
         return 2000;
     }, this);
+    mouse_timer = SDL_AddTimer(100, [](void *userdata, SDL_TimerID, Uint32) -> Uint32 {
+        auto* this_ = (EmuWindow_SDL3*)userdata;
+        this_->input_subsystem->GetMouse()->NotifyChanged();
+        return 100;
+    }, this);
 }
 
 EmuWindow_SDL3::~EmuWindow_SDL3() {
     SDL_RemoveTimer(titlebar_timer);
+    SDL_RemoveTimer(mouse_timer);
     system.HIDCore().UnloadInputDevices();
     input_subsystem->Shutdown();
     SDL_Quit();

src/yuzu_cmd/emu_window/emu_window_sdl3.h

@@ -84,6 +84,9 @@ protected:
     /// Periodic changer of titlebar (independent of event loop)
     SDL_TimerID titlebar_timer;
 
+    // Mouse resetter once it
+    SDL_TimerID mouse_timer;
+
     /// Is the window still open?
     bool is_open = true;