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/lobby/config.go

@@ -5,22 +5,30 @@ import (
 	"time"
 )
 
-// Config configures the matchmaking pool's robot substitution.
+// Config configures auto-match robot substitution: how long an open game waits for a
+// human opponent before a robot is substituted, and how often the reaper scans.
 type Config struct {
-	// RobotWait is how long an auto-match player waits for a human before a robot
-	// is substituted. Sourced from BACKEND_LOBBY_ROBOT_WAIT.
+	// RobotWait is the fixed minimum an open auto-match game waits for a human
+	// opponent before it is eligible for robot substitution. Sourced from
+	// BACKEND_LOBBY_ROBOT_WAIT.
 	RobotWait time.Duration
-	// ReaperInterval is how often the substitution reaper scans for over-waited
-	// players. Sourced from BACKEND_LOBBY_REAPER_INTERVAL.
+	// RobotWaitJitter is a random extra wait in [0, RobotWaitJitter) added on top of
+	// RobotWait per game, so the substitution time varies. Sourced from
+	// BACKEND_LOBBY_ROBOT_WAIT_JITTER.
+	RobotWaitJitter time.Duration
+	// ReaperInterval is how often the reaper scans for open games due for a robot.
+	// Sourced from BACKEND_LOBBY_REAPER_INTERVAL.
 	ReaperInterval time.Duration
 }
 
-// DefaultConfig returns the matchmaking defaults: a 10-second wait
-// (docs/ARCHITECTURE.md §7) scanned every second.
+// DefaultConfig returns the matchmaking defaults: a guaranteed 90-second wait for a
+// human plus up to 90 random seconds (90–180 s total) before a robot substitutes
+// (docs/ARCHITECTURE.md §7), scanned every five seconds.
 func DefaultConfig() Config {
 	return Config{
-		RobotWait:      10 * time.Second,
-		ReaperInterval: time.Second,
+		RobotWait:       90 * time.Second,
+		RobotWaitJitter: 90 * time.Second,
+		ReaperInterval:  5 * time.Second,
 	}
 }
 
@@ -29,6 +37,9 @@ func (c Config) Validate() error {
 	if c.RobotWait <= 0 {
 		return fmt.Errorf("lobby: robot wait must be positive, got %s", c.RobotWait)
 	}
+	if c.RobotWaitJitter < 0 {
+		return fmt.Errorf("lobby: robot wait jitter must not be negative, got %s", c.RobotWaitJitter)
+	}
 	if c.ReaperInterval <= 0 {
 		return fmt.Errorf("lobby: reaper interval must be positive, got %s", c.ReaperInterval)
 	}