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/_components/index.ts

@@ -3,5 +3,6 @@
  */
 
 export * from "./back-button";
+export * from "./avatar-interaction";
 export * from "./character-avatar";
 export * from "./user-message-avatar";