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/__tests__/global-route-context.test.ts

@@ -16,8 +16,8 @@ describe("global route context", () => {
       chatUrl: "/characters/maya/chat",
       splashUrl: "/characters/maya/splash",
     });
-    expect(context.sidebarUrl).toBe(
-      "/sidebar?returnTo=%2Fcharacters%2Fmaya%2Fchat",
+    expect(context.profileUrl).toBe(
+      "/profile?returnTo=%2Fcharacters%2Fmaya%2Fchat",
     );
     expect(context.feedbackUrl).toBe(
       "/feedback?returnTo=%2Fcharacters%2Fmaya%2Fchat",
@@ -52,8 +52,8 @@ describe("global route context", () => {
   });
 
   it("sanitizes return targets when building a global page url", () => {
-    expect(buildGlobalPageUrl(ROUTES.sidebar, "https://example.com")).toBe(
-      "/sidebar?returnTo=%2Fcharacters%2Felio%2Fchat",
+    expect(buildGlobalPageUrl(ROUTES.profile, "https://example.com")).toBe(
+      "/profile?returnTo=%2Fcharacters%2Felio%2Fchat",
     );
   });
 });