[cr149][WIP] ReadingListPageHandler has WebContentsObserver

The brave version of this class was using this observer, but now that
base class has introduced it, we can just rely on that.

Chromium changes:
https://chromium.googlesource.com/chromium/src/+/68cc838450946381bec6c1c777ede5494715f608

commit 68cc838450946381bec6c1c777ede5494715f608
Author: Foromo Daniel Soromou <koretadaniel@chromium.org>
Date:   Tue Apr 21 08:04:31 2026 -0700

    [Side Panel] Fix dangling WebContents pointer in ReadingListPageHandler

    This patch resolves a dangling pointer issue in ReadingListPageHandler
    by replacing the `DanglingUntriaged` raw pointer to
    `content::WebContents` with a `base::WeakPtr<content::WebContents>`.

    Because `WebContents` can be destroyed before the
    `ReadingListPageHandler` (e.g., during teardown), accessing the dangling
    raw pointer could lead to Use-After-Free (UAF) bugs . Null checks have
    been added to safely return early in cases where `web_contents_` has
    already been invalidated.

    Bug: 490505884
    Change-Id: I411121440d26ee770a775eda6d564ea56a385dbf
    Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7775987
    Reviewed-by: Eshwar Stalin <estalin@chromium.org>
    Commit-Queue: Foromo Daniel Soromou <koretadaniel@chromium.org>
    Cr-Commit-Position: refs/heads/main@{#1618202}

browser/ui/webui/side_panel/reading_list/brave_reading_list_page_handler.cc

@@ -17,8 +17,7 @@ BraveReadingListPageHandler::BraveReadingListPageHandler(
     : ReadingListPageHandler(std::move(receiver),
                              std::move(page),
                              reading_list_ui,
-                             web_ui),
-      WebContentsObserver(web_ui->GetWebContents()) {}
+                             web_ui) {}
 
 BraveReadingListPageHandler::~BraveReadingListPageHandler() = default;
 
@@ -33,7 +32,6 @@ void BraveReadingListPageHandler::OnVisibilityChanged(
     // should be called once when web contents is visible after panel is opened.
     // After that, upstream code will update properly for relavant events such
     // as tab change and etc.
-    Observe(nullptr);
     UpdateCurrentPageActionButton();
   }
 }

browser/ui/webui/side_panel/reading_list/brave_reading_list_page_handler.h

@@ -9,14 +9,12 @@
 #include "chrome/browser/ui/webui/side_panel/reading_list/reading_list.mojom.h"
 #include "chrome/browser/ui/webui/side_panel/reading_list/reading_list_page_handler.h"
 #include "content/public/browser/visibility.h"
-#include "content/public/browser/web_contents_observer.h"
 #include "mojo/public/cpp/bindings/pending_receiver.h"
 #include "mojo/public/cpp/bindings/pending_remote.h"
 
 class ReadingListUI;
 
-class BraveReadingListPageHandler : public ReadingListPageHandler,
-                                    public content::WebContentsObserver {
+class BraveReadingListPageHandler : public ReadingListPageHandler {
  public:
   BraveReadingListPageHandler(
       mojo::PendingReceiver<reading_list::mojom::PageHandler> receiver,