fix(ui): keep lobby/game caches fresh across screens (no stale-status flash)

The per-screen in-memory caches (lobbycache, gamecache) were refreshed only by
the screen that owns them while it was mounted, so a state change that crossed
screens left the other screen's cache stale and it visibly redrew on the next
navigation:

- game -> lobby: the player's own move advanced the game cache but not the lobby
  snapshot, and an own move carries no self-directed push event, so returning to
  the lobby painted the pre-move status until the background refresh corrected it.
- lobby -> game (and from any other screen): an opponent's move / game-over
  refreshed the lobby (while mounted) but never the per-game cache, so opening
  that game flashed the pre-move board.

Make cache freshness cross-screen, owned by the single global stream handler
that runs for every live event regardless of the mounted screen:

- patchLobbyGame upserts the affected game's GameView into the lobby snapshot;
  the global handler calls it on opponent_moved / game_over / opponent_joined and
  on a match_found / game_started seed (so a game started elsewhere is present
  too). The game board still mirrors the player's own move and its own load() —
  the two updates no live event carries.
- advanceCached (a pure wrapper over the existing delta reducers) advances a
  not-currently-viewed game's cache from opponent_moved / game_over; the game in
  view is skipped so its mounted board stays the sole owner (no double apply).

End-state behaviour is unchanged (the background refresh always reconciled);
this removes the transient stale frame. Unit-tested patchLobbyGame and
advanceCached; docs/UI_DESIGN.md updated.

docs/UI_DESIGN.md

@@ -48,7 +48,15 @@ Login uses `Screen`.
   collapse to nothing under reduce-motion. Per-game and lobby in-memory caches
   (`lib/gamecache.ts`, `lib/lobbycache.ts`) render a re-opened game or the lobby instantly
   and refresh in the background, removing the blank-loading flash and the lobby's "draw-in"
-  on lobby ↔ game navigation.
+  on lobby ↔ game navigation. The caches are kept fresh **across** screens, so the instant render
+  is already current and not a stale frame the background refresh then corrects. The single global
+  stream handler (`lib/app.svelte.ts`) is the one place that runs for every live event regardless of
+  the mounted screen, so it owns cross-screen freshness: it upserts the affected game's `GameView`
+  into the lobby snapshot (`patchLobbyGame`) on every game event — opponent move, game-over,
+  opponent-joined, and a match/started game (which it also adds) — and advances a not-currently-viewed
+  game's own cache from the move/over delta (`advanceCached`, skipping the game in view, whose mounted
+  board owns its cache). The game board additionally mirrors the player's **own** move and its own
+  `load()` into the lobby snapshot — the two updates no live event carries.
 - **Telegram integration** (`lib/telegram.ts`): inside the Mini App the colour
   scheme is forced from `Telegram.WebApp.colorScheme` (over the OS `prefers-color-scheme`,
   which leaks into the Telegram Desktop webview and otherwise fights it) and the Settings