windows: Track the window display ID locally

Track the current window display ID locally so as not to depend on specific behavior of the video layer, which may change the value at times when it isn't expected.

src/video/windows/SDL_windowsevents.c

@@ -1241,7 +1241,7 @@ WIN_WindowProc(HWND hwnd, UINT msg, WPARAM wParam, LPARAM lParam)
         RECT rect;
         int x, y;
         int w, h;
-        SDL_DisplayID displayID = SDL_GetDisplayForWindow(data->window);
+        const SDL_DisplayID original_displayID = data->last_displayID;
 
         if (data->initializing || data->in_border_change) {
             break;
@@ -1294,7 +1294,10 @@ WIN_WindowProc(HWND hwnd, UINT msg, WPARAM wParam, LPARAM lParam)
         /* Forces a WM_PAINT event */
         InvalidateRect(hwnd, NULL, FALSE);
 
-        if (data->window->last_displayID != displayID) {
+        /* Update the window display position */
+        data->last_displayID = SDL_GetDisplayForWindow(data->window);
+
+        if (data->last_displayID != original_displayID) {
             /* Display changed, check ICC profile */
             WIN_UpdateWindowICCProfile(data->window, SDL_TRUE);
         }

src/video/windows/SDL_windowswindow.c

@@ -309,6 +309,7 @@ static int SetupWindowData(_THIS, SDL_Window *window, HWND hwnd, HWND parent, SD
     data->last_pointer_update = (LPARAM)-1;
     data->videodata = videodata;
     data->initializing = SDL_TRUE;
+    data->last_displayID = window->last_displayID;
     data->scaling_dpi = WIN_GetScalingDPIForHWND(videodata, hwnd);
 
 #ifdef HIGHDPI_DEBUG

src/video/windows/SDL_windowswindow.h

@@ -62,6 +62,7 @@ struct SDL_WindowData
     RECT cursor_clipped_rect;
     SDL_Point last_raw_mouse_position;
     SDL_bool mouse_tracked;
+    SDL_DisplayID last_displayID;
     WCHAR *ICMFileName;
     struct SDL_VideoData *videodata;
 #if SDL_VIDEO_OPENGL_EGL