Controller is not detected after reconnecting (GameSir Cyclone 2, 2.4 GHz)

I'm using a GameSir Cyclone 2 controller on Windows 11 with the 2.4 GHz USB dongle.
If the controller turns off due to inactivity (or disconnects for any reason), I can turn it back on and Windows recognizes it immediately. However, Ship of Harkinian no longer receives any controller input until I completely restart the game.

This doesn't happen in other games I've tested, including other recompilation/port projects, where the controller reconnects normally without restarting the game.

**Steps to reproduce:**
1. Launch Ship of Harkinian.
2. Play using a GameSir Cyclone 2 over the 2.4 GHz dongle.
3. Let the controller power off due to inactivity (or disconnect it).
4. Turn the controller back on.

**Expected behavior:** The game should detect the controller again automatically after it reconnects.

**Actual behavior:** The controller is no longer recognized by the game until Ship of Harkinian is restarted.

System information:
Ship of Harkinian: v9.2.3
OS: Windows 11
Controller: GameSir Cyclone 2 (2.4 GHz USB dongle)

Start by tracing the game's controller-input handling and device reconnect behavior on Windows, using the listed reproduction steps with the GameSir Cyclone 2. Confirm the fix by reconnecting the controller after inactivity or disconnection and verifying that input resumes without restarting Ship of Harkinian.

Written by the indexing model from the issue text.