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.

backend/internal/postgres/migrations/00001_baseline.sql

@@ -96,10 +96,14 @@ CREATE TABLE games (
     created_at        timestamptz NOT NULL DEFAULT now(),
     updated_at        timestamptz NOT NULL DEFAULT now(),
     finished_at       timestamptz,
+    -- open_deadline_at is set only while status='open' (an auto-match game awaiting an
+    -- opponent): the instant the matchmaking reaper substitutes a robot if no human has
+    -- joined by then. NULL for every active and finished game.
+    open_deadline_at  timestamptz,
     dropout_tiles     text        NOT NULL DEFAULT 'remove',
     multiple_words_per_turn boolean NOT NULL DEFAULT true,
     CONSTRAINT games_variant_chk CHECK (variant IN ('scrabble_en', 'scrabble_ru', 'erudit_ru')),
-    CONSTRAINT games_status_chk CHECK (status IN ('active', 'finished')),
+    CONSTRAINT games_status_chk CHECK (status IN ('active', 'finished', 'open')),
     CONSTRAINT games_players_chk CHECK (players BETWEEN 2 AND 4),
     CONSTRAINT games_to_move_chk CHECK (to_move >= 0 AND to_move < players),
     CONSTRAINT games_turn_timeout_chk CHECK (turn_timeout_secs > 0),
@@ -112,15 +116,19 @@ CREATE TABLE games (
 -- The sweeper scans active games oldest-turn-first; a partial index keeps it off the
 -- finished archive.
 CREATE INDEX games_active_idx ON games (turn_started_at) WHERE status = 'active';
+-- The matchmaking reaper scans open games due for a robot substitution; a partial index
+-- keeps it off the active and finished games.
+CREATE INDEX games_open_idx ON games (open_deadline_at) WHERE status = 'open';
 
--- Seats in turn order (seat 0 moves first), one row per player. account_id is a
--- durable account. score is the running/final score, is_winner is stamped on finish
--- (false for every seat on a draw), hints_used counts the per-game allowance consumed
--- before the profile wallet.
+-- Seats in turn order (seat 0 moves first), one row per player. account_id is a durable
+-- account, or NULL for the still-empty opponent seat of an auto-match game waiting for an
+-- opponent (status='open'); it is filled when a human or a robot joins. score is the
+-- running/final score, is_winner is stamped on finish (false for every seat on a draw),
+-- hints_used counts the per-game allowance consumed before the profile wallet.
 CREATE TABLE game_players (
     game_id    uuid     NOT NULL REFERENCES games (game_id) ON DELETE CASCADE,
     seat       smallint NOT NULL,
-    account_id uuid     NOT NULL REFERENCES accounts (account_id),
+    account_id uuid     REFERENCES accounts (account_id),
     score      integer  NOT NULL DEFAULT 0,
     hints_used smallint NOT NULL DEFAULT 0,
     is_winner  boolean  NOT NULL DEFAULT false,