Add “Make my homework”, and finish the mobile polish pass

Homework (/homework — entry points in the drawer and on the create screen)

- Assignment intake reuses the study pipeline: pasted text, photos
  (camera/picker, compressed in the browser) and documents (PDF/DOCX/PPTX/
  ODT/text) through lib/image + lib/documents, the same vision step and the
  same language guard. Raw files never leave the device — only text and JPEG
  data URLs reach the server.
- Two large choice cards: “Just make it” returns the finished homework
  (answer only, plain text, copy + make it again); “Explain how to make this
  homework” builds an interactive guide.
- The guide is one step per screen in the study-feed snap layout:
  explanation, three progressive hints (nudge -> hint -> the answer) and an
  optional checkpoint rendered by the existing activity components (graded
  through /api/grade). The last screen assembles the solution from the step
  answers, with a copy button. Checkpoints carry xp 0 so the guide stays free
  of XP/streak chrome.
- Results live in freezmo.homework.v1 with a small history (open/delete);
  “Make it again” re-runs from the stored assignment text (the vision
  transcription when photos were used) — no original files are stored.
- The answer and the guide are written in the assignment's language, never
  translated into the UI language.

Server

- POST /api/homework: NDJSON stage events like /api/generate, the same
  http-guard, auth checked before parsing, and its own RATE_LIMIT_HOMEWORK
  (documented in .env.example + the README table).
- New prompts in lib/prompts.ts and zod schemas in lib/schemas.ts with the
  same single repair retry; TEXT_MODEL for content, VISION_MODEL only for
  photos. New shared client pieces: useNotesIntake, lib/homework store,
  lib/clipboard, and a shared NDJSON reader in lib/client-api.

Also finishing the mobile polish pass from the previous request

- Phone ice scene: the top-left orb moved behind the glass header (it sat
  behind the page heading/subtitle). The settings sheet's scroll cue is now a
  bare chevron inside a content fade (mask) instead of a chip over the status
  banner, and the API key card's note/disclosure/actions are tightened.
- theme-color now follows the in-app theme (SSR metas still fall back to the
  OS preference); apple-mobile-web-app-status-bar-style stays “default”
  because iOS fixes the status-bar text colour at launch.

Verified: 78/78 homework checks (text/photo/PDF, both modes, EN+CS, dark+light,
360/390px, copy, history persistence, storage privacy, API language, axe), plus
the existing suites re-run (mobile 47/47, pixel contrast 0 below AA, i18n 27/27,
desktop regression 72/72). Lint + build clean; service worker freezmo-v6.

app/homework/page.tsx

@@ -0,0 +1,28 @@
+import { ApiKeyGate } from "@/components/ApiKeyGate";
+import { AppHeader } from "@/components/AppHeader";
+import { HomeworkScreen } from "@/components/homework/HomeworkScreen";
+import { MobileSidebar, Sidebar, SidebarOffset } from "@/components/Sidebar";
+import { TabBar } from "@/components/TabBar";
+
+export const metadata = {
+  title: "Make my homework",
+};
+
+export default function HomeworkPage() {
+  return (
+    <ApiKeyGate>
+      <div className="flex min-h-dvh">
+        <Sidebar />
+        <SidebarOffset />
+        <MobileSidebar />
+        <main className="flex min-h-dvh min-w-0 flex-1 flex-col">
+          <AppHeader />
+          <div className="mx-auto w-full max-w-3xl flex-1 px-4 pb-tabbar lg:px-10 lg:pb-16 lg:pt-10">
+            <HomeworkScreen />
+          </div>
+          <TabBar />
+        </main>
+      </div>
+    </ApiKeyGate>
+  );
+}