[core/hle/services/am] nuke ButtonPoller and Mouse thread (#4229)

Signed-off-by: lizzie <lizzie@eden-emu.dev>

- [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.

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

doesn't even do anything now, please check if controller i/o is affected by this change
this should also fix latency issues with the mouse
the ButtonPoller thread isn't longer required since we update the state immediately with the .on_change callback registered

Reviewed-on: https://git.eden-emu.dev/eden-emu/eden/pulls/4229
Reviewed-by: CamilleLaVey <camillelavey99@gmail.com>

src/input_common/drivers/mouse.h

@@ -1,4 +1,4 @@
-// SPDX-FileCopyrightText: Copyright 2025 Eden Emulator Project
+// SPDX-FileCopyrightText: Copyright 2026 Eden Emulator Project
 // SPDX-License-Identifier: GPL-3.0-or-later
 
 // SPDX-FileCopyrightText: Copyright 2021 yuzu Emulator Project
@@ -93,6 +93,9 @@ public:
 
     void ReleaseAllButtons();
 
+    /// @brief Notifies we changed something about the mouse state and we must update
+    void NotifyChanged();
+
     std::vector<Common::ParamPackage> GetInputDevices() const override;
     AnalogMapping GetAnalogMappingForDevice(const Common::ParamPackage& params) override;
     Common::Input::ButtonNames GetUIName(const Common::ParamPackage& params) const override;
@@ -110,7 +113,6 @@ private:
     Common::Vec3<float> last_motion_change;
     Common::Vec2<int> wheel_position;
     bool button_pressed = false;
-    std::jthread update_thread;
 };
 
 } // namespace InputCommon