feat(profile)!: replace sidebar and add avatar navigation

Rename the global Sidebar route, UI, assets, analytics, and payment return context to Profile. Add accessible message-avatar navigation and preserve the source character across auth and logout flows.

BREAKING CHANGE: /sidebar has been removed; use /profile instead.

src/app/chat/components/chat-header.tsx

@@ -2,11 +2,11 @@
 /**
  * ChatHeader 顶部栏
  *
- * 图标：lucide-react <Lock />（游客 banner）+ <Menu />（菜单按钮）
+ * 图标：lucide-react <Lock />（游客 banner）+ <UserRound />（Profile）
  *   tree-shakable，currentColor 继承父 color
  */
 import type { ReactNode } from "react";
-import { Lock, Menu } from "lucide-react";
+import { Lock, UserRound } from "lucide-react";
 
 import { BackButton } from "@/app/_components";
 import { useActiveCharacterRoutes } from "@/providers/character-provider";
@@ -74,17 +74,17 @@ export function ChatHeader({
 
             <button
               type="button"
-              data-analytics-key="chat.open_menu"
-              data-analytics-label="Open chat menu"
+              data-analytics-key="chat.open_profile"
+              data-analytics-label="Open profile"
               className="flex size-(--responsive-icon-button-size,42px) cursor-pointer items-center justify-center rounded-full border border-[rgba(255,255,255,0.12)] bg-[rgba(13,11,20,0.7)] text-(--color-text-primary,#fff) shadow-[0_10px_24px_rgba(0,0,0,0.2)] backdrop-blur-md transition-[background,transform] duration-150 hover:bg-[rgba(28,24,39,0.82)] active:scale-96 focus-visible:outline-2 focus-visible:outline-offset-3 focus-visible:outline-[#f657a0]"
               onClick={() =>
                 navigator.push(
-                  buildGlobalPageUrl(ROUTES.sidebar, characterRoutes.chat),
+                  buildGlobalPageUrl(ROUTES.profile, characterRoutes.chat),
                 )
               }
-              aria-label="Menu"
+              aria-label="Profile"
             >
-              <Menu size={24} aria-hidden="true" />
+              <UserRound size={24} aria-hidden="true" />
             </button>
           </>
         ) : null}