feat(lobby): enter the game immediately and wait for the opponent inside it

Quick auto-match no longer waits on a separate screen: Enqueue opens a real game seating the caller with an empty opponent seat (new game status 'open') and the player enters it at once. A second human searching the same variant+rule joins that open game; otherwise a background reaper seats a robot after a 90s + random 0-90s wait, pushing a new in-app opponent_joined event that fills the opponent card and re-enables resign and chat in place.

Matchmaking state is now the open games in the database (the in-memory pool, lobby.poll and lobby.cancel are gone), serialised by a per-bucket advisory lock. While a game is open the starter may move on their turn, but resign, chat and nudge are refused; the lobby and opponent card show "searching for opponent".

Schema edited in the baseline (no prod data): 'open' status, nullable game_players.account_id for the empty seat, and a games.open_deadline_at stamp; jet code regenerated.

docs/UI_DESIGN.md

@@ -193,7 +193,12 @@ IV 🏅; active games show Your move 🟢 / Opponent's move ⏳; invitations use
   of starting a game; a lone offered variant is pre-selected, and a bottom **Start game**
   button (disabled until a variant is chosen) confirms. For a **Russian** variant (either
   flow) a **"Multiple words per turn"** checkbox (`.toggle`, **default off** = the single-word
-  rule) appears once that variant is selected; English variants never show it.
+  rule) appears once that variant is selected; English variants never show it. Starting an
+  auto-match **enters the game immediately** and waits inside it: until an opponent joins, the
+  opponent's score card (and the game's lobby row) reads the localized **"searching for opponent"**
+  placeholder, the add-friend 🤝 is hidden, and resign and the chat's send/nudge are disabled; an
+  **opponent_joined** push restores them in place when a human or robot takes the seat, and a line
+  under Start game notes the wait can take a while (the app may be closed meanwhile).
 - **Statistics** (`screens/Stats.svelte`, the lobby 📊 tab): a 2-column grid of stat
   cards (wins / losses / draws / games / win-rate / best game / best move) — pure
   numbers, no charts.