InputText, Nav: fixed remote/shortcut InputText() not teleporting mouse cursor when nav cursor is active and io.ConfigNavMoveSetMousePos is enabled.

Motivated by this, also made SetFocusID() immediately set g.NavIdIsAlive, which is more correct and might be other (positive) subtle side effects.

docs/CHANGELOG.txt

@@ -150,6 +150,9 @@ Other Changes:
       end of a line rather than at the beginning of next line. (#8990, #3237)
   - Fixed low-level word-wrapping function reading from *text_end when passed
     a string range. (#9107) [@achabense]
+- Nav:
+  - Fixed remote/shortcut InputText() not teleporting mouse cursor when
+    nav cursor is visible and `io.ConfigNavMoveSetMousePos` is enabled.
 - Scrollbar: fixed a codepath leading to a divide-by-zero (which would not be
   noticeable by user but detected by sanitizers). (#9089) [@judicaelclair]
 - Added GetItemFlags() in public API for consistency and to expose generic

imgui.cpp

@@ -13055,6 +13055,8 @@ void ImGui::SetFocusID(ImGuiID id, ImGuiWindow* window)
     window->NavLastIds[nav_layer] = id;
     if (g.LastItemData.ID == id)
         window->NavRectRel[nav_layer] = WindowRectAbsToRel(window, g.LastItemData.NavRect);
+    if (g.NavId == g.ActiveId && g.ActiveIdIsAlive)
+        g.NavIdIsAlive = true;
 
     if (g.ActiveIdSource == ImGuiInputSource_Keyboard || g.ActiveIdSource == ImGuiInputSource_Gamepad)
         g.NavHighlightItemUnderNav = true;

imgui_widgets.cpp

@@ -4848,6 +4848,8 @@ bool ImGui::InputTextEx(const char* label, const char* hint, char* buf, int buf_
         SetActiveID(id, window);
         SetFocusID(id, window);
         FocusWindow(window);
+        if (input_requested_by_nav)
+            SetNavCursorVisibleAfterMove();
     }
     if (g.ActiveId == id)
     {