fix(input): inject a no-op input event so force-foreground actually works

Follow-up to the AttachThreadInput change: verified against an isolated repro
(a foreground-stealing window + the helper spawned exactly like the app) that
AttachThreadInput + clearing the foreground-lock timeout was NOT sufficient on
this Windows build - SetForegroundWindow still returned false and Genshin stayed
in the background.

The missing condition is "the calling process received the last input event".
Injecting a benign no-op input (a 0,0 relative mouse move, no cursor movement, no
menu-mnemonic side effect) right before SetForegroundWindow satisfies it. With the
nudge the repro now returns focused:true / setForegroundResult:true from a
background process while another app holds the foreground - the exact auto-scan
start scenario. Applied to both the C# sidecar and the PowerShell fallback.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

native/input-helper/Program.cs

@@ -316,6 +316,12 @@ internal static class Program
             timeoutRead = Native.SystemParametersInfo(Native.SPI_GETFOREGROUNDLOCKTIMEOUT, 0, ref oldTimeout, 0);
             Native.SystemParametersInfo(Native.SPI_SETFOREGROUNDLOCKTIMEOUT, 0, IntPtr.Zero, Native.SPIF_SENDCHANGE);
 
+            // Inject a no-op input (0,0 relative mouse move) so this process counts
+            // as the last input source - one of the conditions Windows requires to
+            // allow a foreground change. This is what the removed ALT tap did, but
+            // without the menu-mnemonic side effect.
+            NudgeInput();
+
             Native.ShowWindowAsync(hwnd, 9); // SW_RESTORE
             Native.BringWindowToTop(hwnd);
             var ok = Native.SetForegroundWindow(hwnd);
@@ -390,6 +396,14 @@ internal static class Program
         return principal.IsInRole(WindowsBuiltInRole.Administrator);
     }
 
+    private static void NudgeInput()
+    {
+        var move = new Native.INPUT[1];
+        move[0].type = 0; // INPUT_MOUSE
+        move[0].mi.dwFlags = Native.MOUSEEVENTF_MOVE; // dx=dy=0 -> no cursor movement
+        Native.SendInput(1, move, Marshal.SizeOf<Native.INPUT>());
+    }
+
     private static uint SendMouseClickBatch()
     {
         var inputs = new Native.INPUT[2];
@@ -427,6 +441,7 @@ internal static class Program
 
 internal static class Native
 {
+    public const uint MOUSEEVENTF_MOVE = 0x0001;
     public const uint MOUSEEVENTF_LEFTDOWN = 0x0002;
     public const uint MOUSEEVENTF_LEFTUP = 0x0004;
     public const uint MOUSEEVENTF_WHEEL = 0x0800;