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/feedback/__tests__/feedback-screen.test.tsx

@@ -69,9 +69,9 @@ describe("FeedbackScreen", () => {
     ).toBe("feedback-content-hint");
     expect(
       container.querySelector<HTMLAnchorElement>(
-        '[data-analytics-key="feedback.back_to_sidebar"]',
+        '[data-analytics-key="feedback.back_to_profile"]',
       )?.getAttribute("href"),
-    ).toBe("/sidebar?returnTo=%2Fcharacters%2Fmaya%2Fchat");
+    ).toBe("/profile?returnTo=%2Fcharacters%2Fmaya%2Fchat");
   });
 
   it("submits valid text and renders the feedback id", async () => {
@@ -106,7 +106,7 @@ describe("FeedbackScreen", () => {
     });
     expect(container.textContent).toContain("feedback-123");
     expect(container.textContent).toContain("Thank you for helping us.");
-    expect(container.textContent).toContain("Back to Sidebar");
+    expect(container.textContent).toContain("Back to Profile");
   });
 });
 

src/app/feedback/feedback-screen.tsx

@@ -77,11 +77,11 @@ export function FeedbackScreen({ returnTo }: FeedbackScreenProps) {
             </div>
             <button
               type="button"
-              data-analytics-key="feedback.back_to_sidebar"
+              data-analytics-key="feedback.back_to_profile"
               className={styles.primaryButton}
-              onClick={() => navigator.replace(navigation.sidebarUrl)}
+              onClick={() => navigator.replace(navigation.profileUrl)}
             >
-              Back to Sidebar
+              Back to Profile
             </button>
           </section>
         </main>
@@ -102,10 +102,10 @@ export function FeedbackScreen({ returnTo }: FeedbackScreenProps) {
 
         <header className={styles.header}>
           <BackButton
-            href={navigation.sidebarUrl}
+            href={navigation.profileUrl}
             variant="soft"
-            ariaLabel="Back to sidebar"
-            analyticsKey="feedback.back_to_sidebar"
+            ariaLabel="Back to profile"
+            analyticsKey="feedback.back_to_profile"
           />
           <div className={styles.headingBlock}>
             <h1 className={styles.title}>Help us improve CozSweet</h1>