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/FillBlank.tsx

@@ -67,7 +67,7 @@ export function isFillBlankCorrect(userValue: string, answer: string): boolean {
   });
 }
 
-export function FillBlank({ activity, active, onAnswered, onNext, isLast }: ActivityComponentProps<FillBlankActivity>) {
+export function FillBlank({ activity, active, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<FillBlankActivity>) {
   const { t } = useI18n();
   const [value, setValue] = useState("");
   const [chosen, setChosen] = useState<string | null>(null);
@@ -185,6 +185,7 @@ export function FillBlank({ activity, active, onAnswered, onNext, isLast }: Acti
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           onNext={onNext}
           detail={
             <span>

components/activities/Flashcard.tsx

@@ -18,7 +18,7 @@ import {
 
 type FlashcardActivity = Extract<Activity, { type: "flashcard" }>;
 
-export function Flashcard({ activity, onAnswered, onNext, isLast }: ActivityComponentProps<FlashcardActivity>) {
+export function Flashcard({ activity, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<FlashcardActivity>) {
   const { t } = useI18n();
   const [flipped, setFlipped] = useState(false);
   const [result, setResult] = useState<boolean | null>(null);
@@ -85,6 +85,7 @@ export function Flashcard({ activity, onAnswered, onNext, isLast }: ActivityComp
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           headline={result ? t("flashcard.frozenSolid") : t("flashcard.keepPile")}
           onNext={onNext}
         />

components/activities/Matching.tsx

@@ -16,7 +16,7 @@ import {
 
 type MatchingActivity = Extract<Activity, { type: "matching" }>;
 
-export function Matching({ activity, onAnswered, onNext, isLast }: ActivityComponentProps<MatchingActivity>) {
+export function Matching({ activity, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<MatchingActivity>) {
   const { t, plural } = useI18n();
   const terms = useMemo(
     () => shuffle(activity.pairs.map((pair, index) => ({ index, text: pair.term }))),
@@ -137,6 +137,7 @@ export function Matching({ activity, onAnswered, onNext, isLast }: ActivityCompo
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           onNext={onNext}
           headline={misses === 0 ? t("matching.perfect") : t("matching.slips")}
           detail={

components/activities/MultipleChoice.tsx

@@ -23,6 +23,7 @@ export function MultipleChoice({
   onAnswered,
   onNext,
   isLast,
+  nextLabel,
 }: ActivityComponentProps<MultipleChoiceActivity>) {
   const { t } = useI18n();
   const [selected, setSelected] = useState<number | null>(null);
@@ -86,6 +87,7 @@ export function MultipleChoice({
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           onNext={onNext}
           detail={
             selected === activity.correctIndex ? null : (

components/activities/Ordering.tsx

@@ -18,7 +18,7 @@ import {
 
 type OrderingActivity = Extract<Activity, { type: "ordering" }>;
 
-export function Ordering({ activity, onAnswered, onNext, isLast }: ActivityComponentProps<OrderingActivity>) {
+export function Ordering({ activity, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<OrderingActivity>) {
   const { t } = useI18n();
   const initial = useMemo(() => shuffle(activity.items), [activity]);
   const [items, setItems] = useState<string[]>(initial);
@@ -126,6 +126,7 @@ export function Ordering({ activity, onAnswered, onNext, isLast }: ActivityCompo
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           onNext={onNext}
         />
       )}

components/activities/ShortAnswer.tsx

@@ -26,7 +26,7 @@ type GradeState =
   | { status: "error"; message: string }
   | { status: "self-check" };
 
-export function ShortAnswer({ activity, active, language, onAnswered, onNext, isLast }: ActivityComponentProps<ShortAnswerActivity>) {
+export function ShortAnswer({ activity, active, language, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<ShortAnswerActivity>) {
   const { t } = useI18n();
   const [value, setValue] = useState("");
   const [state, setState] = useState<GradeState>({ status: "idle" });
@@ -182,6 +182,7 @@ export function ShortAnswer({ activity, active, language, onAnswered, onNext, is
             explanation={activity.explanation}
             xp={activity.xp}
             isLast={isLast}
+          nextLabel={nextLabel}
             onNext={onNext}
           />
         </>

components/activities/TrueFalse.tsx

@@ -17,7 +17,7 @@ import {
 
 type TrueFalseActivity = Extract<Activity, { type: "true_false" }>;
 
-export function TrueFalse({ activity, onAnswered, onNext, isLast }: ActivityComponentProps<TrueFalseActivity>) {
+export function TrueFalse({ activity, onAnswered, onNext, isLast, nextLabel }: ActivityComponentProps<TrueFalseActivity>) {
   const { t } = useI18n();
   const [result, setResult] = useState<boolean | null>(null);
   const x = useMotionValue(0);
@@ -84,6 +84,7 @@ export function TrueFalse({ activity, onAnswered, onNext, isLast }: ActivityComp
           explanation={activity.explanation}
           xp={activity.xp}
           isLast={isLast}
+          nextLabel={nextLabel}
           onNext={onNext}
           detail={
             <span>

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>