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/activities/shared.tsx

@@ -18,6 +18,8 @@ export type ActivityComponentProps<A extends Activity = Activity> = {
   /** Scroll the feed to the next slide. */
   onNext: () => void;
   isLast: boolean;
+  /** Overrides the feedback button label (the homework guide uses this). */
+  nextLabel?: string;
 };
 
 export const TYPE_META: Record<Activity["type"], { labelKey: string; icon: string; tint: string }> = {
@@ -133,6 +135,7 @@ export function FeedbackPanel({
   xp,
   onNext,
   isLast,
+  nextLabel,
   headline,
   detail,
   children,
@@ -142,6 +145,8 @@ export function FeedbackPanel({
   xp?: number;
   onNext: () => void;
   isLast?: boolean;
+  /** Overrides the default “Next” / “See results” label. */
+  nextLabel?: string;
   headline?: string;
   detail?: React.ReactNode;
   children?: React.ReactNode;
@@ -193,7 +198,7 @@ export function FeedbackPanel({
 
       <div className="mt-4 flex items-center justify-end">
         <Button onClick={onNext} size="md" className="min-w-28">
-          {isLast ? t("activity.seeResults") : t("activity.next")}
+          {nextLabel ?? (isLast ? t("activity.seeResults") : t("activity.next"))}
           <span aria-hidden>→</span>
         </Button>
       </div>