fix(seasonal): auto theme re-evaluates over time; auto clears chat background

- The "auto" seasonal theme was computed once at mount, so a long-lived session
  never crossed a season/holiday-window boundary. SeasonalEffect now re-evaluates
  on an hourly ticker (auto mode only) AND refreshes on entering auto — the
  interval only runs while auto, so a stale mount-time timestamp would otherwise
  resurface on a pinned/off → auto switch (the exact frozen-at-mount bug, caught
  in review). The decision is extracted to a pure resolveSeasonTheme(override,
  now) in seasonSchedule.ts (removing an unsafe cast) and unit-tested.

- Selecting seasonal "auto" while a chat background was set was a silent no-op:
  the seasonal picker only cleared the background for a *specific* theme, and the
  overlay is suppressed while a background is set. Now any active seasonal mode
  ("auto" included) clears the background; only "off" leaves it — symmetric with
  the background picker (which sets seasonal "off"). The overlay guard stays as a
  backstop for legacy persisted state.

Bug-hunt findings from LOTUS_TODO. Three review passes (the 2nd caught the
switch-into-auto staleness); +2 unit tests. Gate-green (tsc, eslint, prettier,
922 tests, build).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/app/components/seasonal/seasonSchedule.ts

@@ -93,3 +93,18 @@ export function getActiveSeason(now: Date): SeasonTheme | null {
   const day = now.getDate();
   return SEASON_SCHEDULE.find((entry) => entry.matches(month, day))?.theme ?? null;
 }
+
+/** A seasonal-theme setting value: the active season, a pinned theme, or off. */
+export type SeasonalOverride = SeasonTheme | 'auto' | 'off';
+
+/**
+ * The theme to render for a `seasonalThemeOverride` at time `now` (epoch ms):
+ * 'off' → none, 'auto' → the active season for that instant, else the pinned
+ * theme. Kept pure (and unit-tested) so the decision is verifiable without
+ * mounting the React overlay.
+ */
+export function resolveSeasonTheme(override: SeasonalOverride, now: number): SeasonTheme | null {
+  if (override === 'off') return null;
+  if (override === 'auto') return getActiveSeason(new Date(now));
+  return override;
+}