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/homework/HomeworkHistory.tsx

@@ -0,0 +1,89 @@
+"use client";
+
+import { useState } from "react";
+
+import { ChevronRightIcon, XIcon } from "@/components/icons";
+import { Button } from "@/components/ui";
+import { homeworkModeLabelKey } from "@/lib/homework";
+import { useI18n } from "@/lib/i18n";
+import type { HomeworkRecord } from "@/lib/schemas";
+
+/** Small history list under the input: open a past result or delete it. */
+export function HomeworkHistory({
+  records,
+  onOpen,
+  onDelete,
+}: {
+  records: HomeworkRecord[];
+  onOpen: (record: HomeworkRecord) => void;
+  onDelete: (id: string) => void;
+}) {
+  const { locale, t } = useI18n();
+  const [confirmId, setConfirmId] = useState<string | null>(null);
+
+  if (records.length === 0) return null;
+
+  return (
+    <section className="space-y-2">
+      <h2 className="text-[15px] font-semibold tracking-[-0.01em] text-[var(--text)]">
+        {t("homework.history.title")}
+      </h2>
+      <ul className="list-group">
+        {records.map((record) =>
+          confirmId === record.id ? (
+            <li key={record.id} className="flex flex-wrap items-center justify-between gap-2 px-3 py-2.5">
+              <span className="text-[12.5px] font-medium text-[var(--text-muted)]">
+                {t("homework.history.deleteConfirm")}
+              </span>
+              <span className="flex shrink-0 items-center gap-1">
+                <Button
+                  size="sm"
+                  variant="danger"
+                  className="touch-target"
+                  onClick={() => {
+                    onDelete(record.id);
+                    setConfirmId(null);
+                  }}
+                >
+                  {t("common.delete")}
+                </Button>
+                <Button size="sm" variant="ghost" className="touch-target" onClick={() => setConfirmId(null)}>
+                  {t("common.cancel")}
+                </Button>
+              </span>
+            </li>
+          ) : (
+            <li key={record.id} className="flex items-center gap-1 px-1.5 py-1.5">
+              <button
+                type="button"
+                onClick={() => onOpen(record)}
+                aria-label={t("homework.history.openTitle", { title: record.title })}
+                className="flex min-w-0 flex-1 items-center gap-3 rounded-xl px-2 py-1.5 text-left transition hover:bg-[var(--hover)]"
+              >
+                <span className="min-w-0 flex-1">
+                  <span className="block truncate text-[13.5px] font-medium text-[var(--text)]">{record.title}</span>
+                  <span className="block text-[11.5px] text-[var(--text-subtle)]">
+                    {t(homeworkModeLabelKey(record.mode))} ·{" "}
+                    {new Date(record.updatedAt).toLocaleDateString(locale === "cs" ? "cs-CZ" : "en-US", {
+                      day: "numeric",
+                      month: "short",
+                    })}
+                  </span>
+                </span>
+                <ChevronRightIcon className="size-4 shrink-0 text-[var(--text-subtle)]" />
+              </button>
+              <button
+                type="button"
+                onClick={() => setConfirmId(record.id)}
+                aria-label={`${t("common.delete")} — ${record.title}`}
+                className="touch-target grid size-9 shrink-0 place-items-center rounded-lg text-[var(--text-subtle)] transition hover:bg-[var(--hover)] hover:text-rose-600 dark:hover:text-rose-300"
+              >
+                <XIcon className="size-4" />
+              </button>
+            </li>
+          ),
+        )}
+      </ul>
+    </section>
+  );
+}