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/__tests__/use-pwa-install-entry.test.ts

@@ -0,0 +1,45 @@
+import { describe, expect, it } from "vitest";
+
+import { shouldKeepPwaInstallEntryVisible } from "../use-pwa-install-entry";
+
+describe("shouldKeepPwaInstallEntryVisible", () => {
+  it("hides the install entry after accepted installs", () => {
+    expect(
+      shouldKeepPwaInstallEntryVisible({
+        result: "accepted",
+        isInstalled: true,
+        canShowInstallEntry: true,
+      }),
+    ).toBe(false);
+  });
+
+  it("keeps the install entry after dismissed prompts when still available", () => {
+    expect(
+      shouldKeepPwaInstallEntryVisible({
+        result: "dismissed",
+        isInstalled: false,
+        canShowInstallEntry: true,
+      }),
+    ).toBe(true);
+  });
+
+  it("keeps the install entry after unavailable prompts when still available", () => {
+    expect(
+      shouldKeepPwaInstallEntryVisible({
+        result: "unavailable",
+        isInstalled: false,
+        canShowInstallEntry: true,
+      }),
+    ).toBe(true);
+  });
+
+  it("hides the install entry when the platform can no longer show it", () => {
+    expect(
+      shouldKeepPwaInstallEntryVisible({
+        result: "dismissed",
+        isInstalled: false,
+        canShowInstallEntry: false,
+      }),
+    ).toBe(false);
+  });
+});