Migrate component state to Jotai atoms across settings, explore, and dashboard

Replace ad-hoc useState/useEffect fetch patterns with Jotai atoms and
loadables in StatsDisplay, FilterableTitleRow, BackupScheduleSection,
IntegrationsSection, and CommandPalette. Each component now gets a
scoped Jotai Provider with a pre-initialized store so server-rendered
initial values hydrate correctly. Async data fetching moves into
atom-level loadables, eliminating manual loading flags and cancellation
logic throughout.

lib/atoms/stats.ts

@@ -0,0 +1,29 @@
+import { atom } from "jotai";
+import { loadable } from "jotai/utils";
+import type { HistoryBucket, TimePeriod } from "@/lib/services/discovery";
+
+export const moviePeriodAtom = atom<TimePeriod>("this_month");
+export const episodePeriodAtom = atom<TimePeriod>("this_week");
+
+async function fetchStats(
+  type: "movies" | "episodes",
+  period: TimePeriod,
+): Promise<{ count: number; history: HistoryBucket[] }> {
+  const res = await fetch(
+    `/api/stats?type=${type}&period=${period}&history=true`,
+  );
+  return res.json();
+}
+
+const movieStatsAsyncAtom = atom(async (get) => {
+  const period = get(moviePeriodAtom);
+  return fetchStats("movies", period);
+});
+
+const episodeStatsAsyncAtom = atom(async (get) => {
+  const period = get(episodePeriodAtom);
+  return fetchStats("episodes", period);
+});
+
+export const movieStatsLoadable = loadable(movieStatsAsyncAtom);
+export const episodeStatsLoadable = loadable(episodeStatsAsyncAtom);