[iOS] - Fix private-mode/normal-mode flip when opening tabs (uplift t…

…o 1.73.x) (#26638)

Uplift of #26621 (squashed) to release

ios/brave-ios/Sources/Brave/Frontend/Browser/BrowserViewController/BrowserViewController.swift

@@ -2171,7 +2171,12 @@ public class BrowserViewController: UIViewController {
     let request: URLRequest?
     if let url = url {
       // If only empty tab present, the url will open in existing tab
-      if tabManager.isBrowserEmptyForCurrentMode {
+      // We also need to respect private browsing mode when opening URLs directly.
+      // If the only tab open is NTP, AND the private mode matches that of the tab request,
+      // only then we can open the tab directly.
+      if tabManager.isBrowserEmptyForCurrentMode
+        && tabManager.privateBrowsingManager.isPrivateBrowsing == isPrivate
+      {
         finishEditingAndSubmit(url)
         return
       }

ios/brave-ios/Sources/Brave/Frontend/Browser/TabManager.swift

@@ -333,10 +333,9 @@ class TabManager: NSObject {
     if previous === tab {
       return
     }
-    // Convert the global mode to private if opening private tab from normal tab/ history/bookmark.
-    if selectedTab?.isPrivate != true && tab?.isPrivate == true {
-      privateBrowsingManager.isPrivateBrowsing = true
-    }
+    // Convert the global mode to normal/private
+    privateBrowsingManager.isPrivateBrowsing = tab?.isPrivate == true
+
     // Make sure to wipe the private tabs if the user has the pref turned on
     if !TabType.of(tab).isPrivate
       && (Preferences.Privacy.privateBrowsingOnly.value