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/coins-rules/__tests__/coins-rules-screen.test.tsx

@@ -22,14 +22,14 @@ vi.mock("@/stores/user/user-context", () => ({
 }));
 
 describe("CoinsRulesScreen", () => {
-  it("renders outside CharacterProvider and returns to global sidebar", () => {
+  it("renders outside CharacterProvider and returns to global profile", () => {
     const html = renderToStaticMarkup(
       <CoinsRulesScreen returnTo="/characters/maya/chat" />,
     );
 
     expect(html).toContain("Coin Usage Rules");
     expect(html).toContain(
-      'href="/sidebar?returnTo=%2Fcharacters%2Fmaya%2Fchat"',
+      'href="/profile?returnTo=%2Fcharacters%2Fmaya%2Fchat"',
     );
   });
 });

src/app/coins-rules/coins-rules-screen.tsx

@@ -118,9 +118,9 @@ export function CoinsRulesScreen({ returnTo }: CoinsRulesScreenProps) {
       <main className={styles.screen}>
         <header className={styles.header}>
           <BackButton
-            href={navigation.sidebarUrl}
+            href={navigation.profileUrl}
             variant="soft"
-            aria-label="Back to sidebar"
+            aria-label="Back to profile"
           />
 
           <div className={styles.hero}>