Prevent loading sync ui in private window

Currently, brave sync ui isn't allowed to load in private window.
That only works properly in normal window.

browser/brave_scheme_load_browsertest.cc

@@ -237,3 +237,10 @@ IN_PROC_BROWSER_TEST_F(BraveSchemeLoadBrowserTest, NotAllowedInPrivateWindow) {
   TestURLIsNotLoadedInPrivateWindow(GURL("brave://settings/"),
                                     GURL("chrome://settings/"));
 }
+
+// Check brave sync page is also not loaded in private widnow.
+IN_PROC_BROWSER_TEST_F(BraveSchemeLoadBrowserTest,
+                       SyncUINotAllowedInPrivateWindow) {
+  TestURLIsNotLoadedInPrivateWindow(GURL("brave://sync/"),
+                                    GURL("chrome://sync/"));
+}

patches/chrome-browser-ui-browser_navigator.cc.patch

@@ -0,0 +1,21 @@
+diff --git a/chrome/browser/ui/browser_navigator.cc b/chrome/browser/ui/browser_navigator.cc
+index 57cc96c276c1106079828b5e359a3d88e1c901ce..81baaee0fdad10d4b1f4dc17889a44550083ee46 100644
+--- a/chrome/browser/ui/browser_navigator.cc
++++ b/chrome/browser/ui/browser_navigator.cc
+@@ -707,6 +707,16 @@ bool IsHostAllowedInIncognito(const GURL& url) {
+            host != chrome::kChromeUISuggestionsHost;
+   }
+
++#if defined(BRAVE_CHROMIUM_BUILD)
++  DCHECK(!url.SchemeIs(content::kBraveUIScheme))
++      << "brave url should not be reached here. scheme mapping should be done "
++         "before. Use chrome scheme for this url: "
++      << url.spec();
++  // sync page is not allowed in private window.
++  if (host == kBraveUISyncHost)
++    return false;
++#endif
++
+   if (scheme != content::kChromeUIScheme)
+     return true;
+