[Code health] Convert /chrome/browser/ui/webui/media_router away from WebUI::RegisterDeprecatedMessageCallback

...to WebUI::RegisterMessageCallback. (In some cases some other deprecated
usages were converted, when fairly local).

This CL was uploaded by git cl split.

Bug: 1243386
Change-Id: I344706cee8331bb83a38c09f7f84951c13484da0
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3732475
Reviewed-by: Muyao Xu <muyaoxu@google.com>
Auto-Submit: Maks Orlovich <morlovich@chromium.org>
Commit-Queue: Muyao Xu <muyaoxu@google.com>
Cr-Commit-Position: refs/heads/main@{#1021282}
diff --git a/chrome/browser/ui/webui/media_router/cast_feedback_ui.cc b/chrome/browser/ui/webui/media_router/cast_feedback_ui.cc
index 2fd1b7e..52fabfdc 100644
--- a/chrome/browser/ui/webui/media_router/cast_feedback_ui.cc
+++ b/chrome/browser/ui/webui/media_router/cast_feedback_ui.cc
@@ -175,7 +175,7 @@
 
   content::WebUIDataSource::Add(profile_, source);
 
-  web_ui->RegisterDeprecatedMessageCallback(
+  web_ui->RegisterMessageCallback(
       "close", base::BindRepeating(&CastFeedbackUI::OnCloseMessage,
                                    base::Unretained(this)));
   web_ui->AddMessageHandler(std::make_unique<MetricsHandler>());
@@ -185,7 +185,7 @@
 
 CastFeedbackUI::~CastFeedbackUI() = default;
 
-void CastFeedbackUI::OnCloseMessage(const base::ListValue*) {
+void CastFeedbackUI::OnCloseMessage(const base::Value::List&) {
   web_contents_->GetDelegate()->CloseContents(web_contents_);
 }
 
diff --git a/chrome/browser/ui/webui/media_router/cast_feedback_ui.h b/chrome/browser/ui/webui/media_router/cast_feedback_ui.h
index 0139c22..16b6a7a 100644
--- a/chrome/browser/ui/webui/media_router/cast_feedback_ui.h
+++ b/chrome/browser/ui/webui/media_router/cast_feedback_ui.h
@@ -6,14 +6,11 @@
 #define CHROME_BROWSER_UI_WEBUI_MEDIA_ROUTER_CAST_FEEDBACK_UI_H_
 
 #include "base/memory/raw_ptr.h"
+#include "base/values.h"
 #include "content/public/browser/web_ui_controller.h"
 
 class Profile;
 
-namespace base {
-class ListValue;
-}
-
 namespace content {
 class WebContents;
 class WebUI;
@@ -29,7 +26,7 @@
   ~CastFeedbackUI() override;
 
  private:
-  void OnCloseMessage(const base::ListValue*);
+  void OnCloseMessage(const base::Value::List&);
 
   const raw_ptr<Profile> profile_;
   const raw_ptr<content::WebContents> web_contents_;