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/router/routes.ts

@@ -25,7 +25,7 @@ export const ROUTES = {
   tip: "/tip",
   externalEntry: "/external-entry",
   auth: "/auth",
-  sidebar: "/sidebar",
+  profile: "/profile",
   feedback: "/feedback",
   subscription: "/subscription",
   coinsRules: "/coins-rules",
@@ -114,7 +114,7 @@ export const ALL_STATIC_ROUTES: readonly StaticRoute[] = [
   ROUTES.tip,
   ROUTES.externalEntry,
   ROUTES.auth,
-  ROUTES.sidebar,
+  ROUTES.profile,
   ROUTES.feedback,
   ROUTES.coinsRules,
 ] as const;