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.

components/ThemeToggle.tsx

@@ -8,6 +8,28 @@ import { MoonIcon, SunIcon } from "@/components/icons";
 
 const STORAGE_KEY = "freezmo.theme";
 
+const THEME_COLORS = { light: "#f4f7fd", dark: "#0e1424" } as const;
+
+/**
+ * Keeps the first `theme-color` meta (the one the app owns) in step with the
+ * in-app theme. The SSR metas follow the OS preference; this one always wins
+ * because it is media-less and first in the head.
+ */
+export function syncThemeColor(theme: "light" | "dark") {
+  try {
+    let meta = document.querySelector<HTMLMetaElement>('meta[name="theme-color"][data-app]');
+    if (!meta) {
+      meta = document.createElement("meta");
+      meta.setAttribute("name", "theme-color");
+      meta.setAttribute("data-app", "1");
+      document.head.insertBefore(meta, document.head.firstChild);
+    }
+    meta.setAttribute("content", THEME_COLORS[theme]);
+  } catch {
+    /* private mode / odd embedded browsers */
+  }
+}
+
 export function useTheme() {
   const [theme, setTheme] = useState<"light" | "dark">("light");
 
@@ -17,11 +39,13 @@ export function useTheme() {
       ? stored === "dark"
       : window.matchMedia("(prefers-color-scheme: dark)").matches;
     setTheme(isDark ? "dark" : "light");
+    syncThemeColor(isDark ? "dark" : "light");
   }, []);
 
   const apply = (next: "light" | "dark") => {
     setTheme(next);
     document.documentElement.classList.toggle("dark", next === "dark");
+    syncThemeColor(next);
     try {
       window.localStorage.setItem(STORAGE_KEY, next);
     } catch {