fix(startup): hide the taskbar proxy too, and trace the --tray timeline

The window still showed, taskbar entry included. Two things.

The taskbar button belongs to the FMX proxy window (TFMAppClass), a separate
top-level window from the form — hiding the form alone never removed it.
FindFMXAppWindow moves from private to public so the activate-hide can drop
both. (Guarded on Assigned(FBridge): the handler is installed at line 222,
the bridge is created at 268.)

And rather than guess a fourth time at FMX's startup order — the same trap as
the window-state saga, which only fell to instrumentation — this logs a
millisecond timeline: FormCreate begin/end, the activate-hide, and the
deferred MinimizeToTray. Whichever gap holds the second will be obvious.

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

delphi-backend/Source/PM.Bridge.pas

@@ -140,8 +140,11 @@ type
     procedure PrepareNid;
     procedure ShowTrayMenu;
     procedure ShowFirstTimeBalloon;
-    function FindFMXAppWindow: HWND;
   public
+    // The FMX taskbar proxy (TFMAppClass) — a SEPARATE top-level window from
+    // the form, and the one that owns the taskbar entry. Public so the host
+    // can hide it during a --tray launch, before MinimizeToTray gets to run.
+    function FindFMXAppWindow: HWND;
     // Tray balloon (caller applies its own gating setting). Used for
     // messages the user must see while the window is hidden — e.g. an
     // autofill blocked by an elevated target.

delphi-backend/UMainForm.pas

@@ -220,6 +220,7 @@ begin
   begin
     Visible    := False;
     OnActivate := TrayStartupHideOnce;
+    LogLine('[tray] FormCreate begin at ' + FormatDateTime('hh:nn:ss.zzz', Now));
   end;
 
   // The .fmx ships WindowState = wsMaximized, so that is the starting intent.
@@ -325,11 +326,13 @@ begin
     // it's noise when Windows itself put us in the tray (the user
     // didn't actively minimise). Manual launches still see it once.
     FBridge.BalloonShown := True;
+    LogLine('[tray] FormCreate end at ' + FormatDateTime('hh:nn:ss.zzz', Now));
     TThread.ForceQueue(nil,
       procedure
       begin
         FBridge.MinimizeToTray;
-        LogLine('Launched with --tray, minimised at startup (balloon suppressed)');
+        LogLine('[tray] deferred MinimizeToTray ran at ' +
+                FormatDateTime('hh:nn:ss.zzz', Now));
       end);
   end;
 end;
@@ -1600,13 +1603,22 @@ end;
 
 procedure TMainForm.TrayStartupHideOnce(Sender: TObject);
 var
-  LHwnd: HWND;
+  LHwnd, LAppHwnd: HWND;
 begin
   OnActivate := nil;          // one shot — never fight the user afterwards
   Visible := False;
   LHwnd := WindowHandleToPlatform(Self.Handle).Wnd;
   if LHwnd <> 0 then
     ShowWindow(LHwnd, SW_HIDE);
+  // The taskbar entry belongs to the FMX proxy window, not the form — hiding
+  // the form alone leaves the button on the taskbar.
+  if Assigned(FBridge) then
+  begin
+    LAppHwnd := FBridge.FindFMXAppWindow;
+    if LAppHwnd <> 0 then ShowWindow(LAppHwnd, SW_HIDE);
+  end;
+  LogLine('[tray] activate-hide fired at ' +
+          FormatDateTime('hh:nn:ss.zzz', Now));
 end;
 
 // Single entry point for every tray restore. ExecuteAutofill really minimises