Fix the mode-choice redundancy: standardized names, deep links, compact switch

Terminology (lib/i18n-dict.ts)
- One name per mode everywhere: "Study Deck" / "Studijní balíček" and
  "Homework Solver" / "Řešitel úkolů". The library empty-state cards and the
  /create switcher now read the same, so the choice no longer changes name
  between screens.

Deep links
- Library quick actions carry the mode: /create?mode=deck and
  /homework?mode=homework.
- Both pages canonicalize: /create?mode=homework redirects to the homework
  flow and /homework?mode=deck redirects to /create, so a mode link always
  opens that mode directly.

/create
- The two bulky square cards (106px tall, wrapping/clipping "Study Deck &
  Qu…" on phones) are replaced by a compact segmented control (52px) placed
  directly above "1. Add your notes": ice pill, snowflake/sparkles icons,
  44px segments and one-line labels at 360px. The pill slides to the chosen
  segment and the route follows ~190ms later, so toggling reads as one smooth
  transition (immediate under prefers-reduced-motion).

Service worker: freezmo-v9.

Verified: mode-switch suite 26/26 (deep links, cross-mode redirects, 52px
control, 44px segments, no clipping/wrapping at 360px, "1. Add your notes" at
y=394 of 740 with the upload controls above the fold, pill slide, axe contrast,
en+cs, phone+desktop), mobile 49/49, i18n 27/27, desktop regression 73/73.
Lint + build clean.

components/LibraryScreen.tsx

@@ -228,7 +228,7 @@ export function LibraryScreen() {
                assignment. Stacked on phones, side by side from 640px up. */
             <div className="grid w-[min(24rem,calc(100vw_-_3rem))] gap-3 sm:w-[36rem] sm:grid-cols-2">
               <Link
-                href="/create"
+                href="/create?mode=deck"
                 className="card card-hover touch-target flex items-center gap-3 border-accent-400/60 p-3.5 text-left sm:p-4"
               >
                 <span
@@ -242,7 +242,7 @@ export function LibraryScreen() {
                 </span>
               </Link>
               <Link
-                href="/homework"
+                href="/homework?mode=homework"
                 className="card card-hover touch-target flex items-center gap-3 p-3.5 text-left sm:p-4"
               >
                 <span

components/ModeSwitch.tsx

@@ -0,0 +1,80 @@
+"use client";
+
+import { useRouter } from "next/navigation";
+import { useEffect, useRef, useState } from "react";
+
+import { SnowflakeIcon, SparklesIcon } from "@/components/icons";
+import { useI18n } from "@/lib/i18n";
+import { cn } from "@/lib/utils";
+
+export type StudyMode = "deck" | "homework";
+
+/** Canonical URL per mode, so a deep link always lands on the right screen. */
+export const MODE_HREF: Record<StudyMode, string> = {
+  deck: "/create?mode=deck",
+  homework: "/homework?mode=homework",
+};
+
+/** How long the ice pill takes to slide before the route follows. */
+const SLIDE_MS = 180;
+
+/**
+ * Compact two-segment mode switch (Study Deck / Homework Solver). The ice pill
+ * slides to the chosen segment and the router follows a moment later, so the
+ * toggle reads as one smooth transition instead of a hard jump. The current
+ * mode stays pressed; the other segment navigates.
+ */
+export function ModeSwitch({ current }: { current: StudyMode }) {
+  const { t } = useI18n();
+  const router = useRouter();
+  const [pending, setPending] = useState<StudyMode | null>(null);
+  const timer = useRef<number | null>(null);
+
+  useEffect(
+    () => () => {
+      if (timer.current !== null) window.clearTimeout(timer.current);
+    },
+    [],
+  );
+
+  const choose = (mode: StudyMode) => {
+    if (mode === current || pending !== null) return;
+    setPending(mode);
+    const reduce = window.matchMedia("(prefers-reduced-motion: reduce)").matches;
+    timer.current = window.setTimeout(() => router.push(MODE_HREF[mode]), reduce ? 0 : SLIDE_MS + 10);
+  };
+
+  const shown = pending ?? current;
+
+  const segment = (mode: StudyMode, icon: React.ReactNode, label: string) => (
+    <button
+      type="button"
+      aria-pressed={current === mode}
+      onClick={() => choose(mode)}
+      className={cn(
+        "relative z-10 inline-flex min-h-11 items-center justify-center gap-1.5 rounded-xl px-2 text-[13.5px] font-semibold transition-colors",
+        shown === mode ? "text-[#06111f]" : "text-frost-700 hover:text-[var(--text)] dark:text-frost-300",
+      )}
+    >
+      {icon}
+      <span className="whitespace-nowrap">{label}</span>
+    </button>
+  );
+
+  return (
+    <div
+      data-testid="mode-switch"
+      className="relative grid grid-cols-2 rounded-[0.95rem] border border-[var(--hairline)] bg-[var(--surface-sunken)] p-[3px] backdrop-blur-sm"
+    >
+      <span
+        aria-hidden
+        className={cn(
+          "grad-ice pointer-events-none absolute inset-y-[3px] left-[3px] w-[calc(50%-3px)] rounded-xl shadow-[0_6px_16px_-8px_rgb(56_189_248/0.7)] transition-transform duration-[180ms] ease-out motion-reduce:transition-none",
+          shown === "homework" && "translate-x-full",
+        )}
+      />
+      {segment("deck", <SnowflakeIcon className="size-4" />, t("actionStudyDeck"))}
+      {segment("homework", <SparklesIcon className="size-4" />, t("actionHomework"))}
+    </div>
+  );
+}

components/UploadScreen.tsx

@@ -1,7 +1,6 @@
 "use client";
 
 import { motion } from "framer-motion";
-import Link from "next/link";
 import { useRouter } from "next/navigation";
 import { useCallback, useEffect, useMemo, useRef, useState, useSyncExternalStore } from "react";
 
@@ -33,7 +32,8 @@ import { UNORGANIZED_ID, type Difficulty } from "@/lib/schemas";
 import { upsertDeck } from "@/lib/storage";
 import { openSettings } from "@/lib/ui-events";
 import { cn, uid } from "@/lib/utils";
-import { CameraIcon, FolderIcon, IceCubeIcon, PlusIcon, SnowflakeIcon, SparklesIcon, SunIcon } from "@/components/icons";
+import { CameraIcon, FolderIcon, IceCubeIcon, PlusIcon, SnowflakeIcon, SunIcon } from "@/components/icons";
+import { ModeSwitch } from "@/components/ModeSwitch";
 import { Button, ProgressBar } from "@/components/ui";
 
 type Phase = "idle" | "preparing" | "loading" | "error";
@@ -321,39 +321,9 @@ export function UploadScreen() {
           </p>
         </section>
 
-        {/* Mode switcher: this page builds a study deck from notes; the other
-            card hands the same intake over to the homework flow. */}
-        <div className="grid grid-cols-2 gap-2.5 sm:gap-3">
-          <Link
-            href="/create"
-            aria-current="page"
-            className="card touch-target flex flex-col items-start gap-2 rounded-2xl border-accent-400/60 bg-accent-50/60 p-3 ring-2 ring-accent-400/30 sm:flex-row sm:items-center sm:gap-3 sm:p-3.5 dark:bg-accent-500/15"
-          >
-            <span
-              aria-hidden
-              className="grad-ice grid size-9 shrink-0 place-items-center rounded-xl text-[#06111f]"
-            >
-              <SnowflakeIcon className="size-5" />
-            </span>
-            <span className="min-w-0 text-[13px] font-semibold leading-snug text-[var(--text)] sm:text-[13.5px]">
-              {t("actionStudyDeck")}
-            </span>
-          </Link>
-          <Link
-            href="/homework"
-            className="card card-hover touch-target flex flex-col items-start gap-2 rounded-2xl p-3 sm:flex-row sm:items-center sm:gap-3 sm:p-3.5"
-          >
-            <span
-              aria-hidden
-              className="grid size-9 shrink-0 place-items-center rounded-xl bg-[var(--surface-sunken)] text-[var(--text-muted)]"
-            >
-              <SparklesIcon className="size-5" />
-            </span>
-            <span className="min-w-0 text-[13px] font-semibold leading-snug text-[var(--text)] sm:text-[13.5px]">
-              {t("actionHomework")}
-            </span>
-          </Link>
-        </div>
+        {/* Mode switcher: a compact segmented control. This page is the Study
+            Deck side; the other segment opens the homework flow. */}
+        <ModeSwitch current="deck" />
 
 
         {error ? (