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/profile/use-pwa-install-entry.ts

@@ -0,0 +1,54 @@
+"use client";
+
+import { useEffect, useState } from "react";
+
+import { pwaUtil } from "@/utils/pwa";
+
+type PwaInstallResult = Awaited<ReturnType<typeof pwaUtil.install>>;
+
+export function usePwaInstallEntry() {
+  const [canInstall, setCanInstall] = useState(false);
+
+  useEffect(() => {
+    const updateInstallEntryVisibility = () => {
+      setCanInstall(pwaUtil.canShowInstallEntry());
+    };
+
+    pwaUtil.prepareInstallPrompt();
+    updateInstallEntryVisibility();
+    const unsubscribe = pwaUtil.subscribe(updateInstallEntryVisibility);
+
+    return () => {
+      unsubscribe();
+    };
+  }, []);
+
+  const installApp = async () => {
+    pwaUtil.prepareInstallPrompt();
+    const result = await pwaUtil.install();
+    setCanInstall(
+      shouldKeepPwaInstallEntryVisible({
+        result,
+        isInstalled: pwaUtil.isInstalled(),
+        canShowInstallEntry: pwaUtil.canShowInstallEntry(),
+      }),
+    );
+  };
+
+  return {
+    canInstall,
+    installApp,
+  };
+}
+
+export function shouldKeepPwaInstallEntryVisible({
+  result,
+  isInstalled,
+  canShowInstallEntry,
+}: {
+  result: PwaInstallResult;
+  isInstalled: boolean;
+  canShowInstallEntry: boolean;
+}): boolean {
+  return result !== "accepted" && !isInstalled && canShowInstallEntry;
+}