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.

lib/clipboard.ts

@@ -0,0 +1,37 @@
+"use client";
+
+/**
+ * Copy text to the clipboard.
+ *
+ * `navigator.clipboard` only exists in a secure context, and Freezmo is often
+ * used over plain http on a LAN, so fall back to the classic hidden-textarea
+ * trick. Returns false when neither path works (the caller can then tell the
+ * user to copy manually).
+ */
+export async function copyText(text: string): Promise<boolean> {
+  try {
+    if (typeof navigator !== "undefined" && navigator.clipboard && window.isSecureContext) {
+      await navigator.clipboard.writeText(text);
+      return true;
+    }
+  } catch {
+    /* fall through to the legacy path */
+  }
+
+  try {
+    const area = document.createElement("textarea");
+    area.value = text;
+    area.setAttribute("readonly", "");
+    area.style.position = "fixed";
+    area.style.top = "0";
+    area.style.opacity = "0";
+    document.body.appendChild(area);
+    area.focus();
+    area.select();
+    const ok = document.execCommand("copy");
+    area.remove();
+    return ok;
+  } catch {
+    return false;
+  }
+}