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/lib/analytics/__tests__/payment_analytics_context.test.ts

@@ -30,10 +30,10 @@ describe("payment analytics context", () => {
 
     expect(
       parsePaymentAnalyticsContext({
-        entryPoint: "sidebar",
+        entryPoint: "profile",
         triggerReason: null,
         subscriptionType: "vip",
       }),
-    ).toEqual({ entryPoint: "sidebar", triggerReason: "vip_cta" });
+    ).toEqual({ entryPoint: "profile", triggerReason: "vip_cta" });
   });
 });