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/server/dto.go

@@ -1,6 +1,8 @@
 package server
 
 import (
+	"github.com/google/uuid"
+
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/game"
@@ -186,9 +188,16 @@ const awayTimeLayout = "15:04"
 func gameDTOFromGame(g game.Game) gameDTO {
 	seats := make([]seatDTO, 0, len(g.Seats))
 	for _, s := range g.Seats {
+		// An open game's still-empty opponent seat has no account: emit an empty id (the
+		// display name is left empty by fillSeatNames) so the client shows "searching for
+		// opponent" rather than the nil-UUID.
+		accountID := ""
+		if s.AccountID != uuid.Nil {
+			accountID = s.AccountID.String()
+		}
 		seats = append(seats, seatDTO{
 			Seat:      s.Seat,
-			AccountID: s.AccountID.String(),
+			AccountID: accountID,
 			Score:     s.Score,
 			HintsUsed: s.HintsUsed,
 			IsWinner:  s.IsWinner,
@@ -277,13 +286,12 @@ func stateDTOFrom(v game.StateView, includeAlphabet bool) (stateDTO, error) {
 	return dto, nil
 }
 
-// matchDTOFrom projects an enqueue/poll result into its DTO.
+// matchDTOFrom projects an enqueue result into its DTO. Enqueue always lands the
+// caller in a game (freshly opened or joined), so the game is always present; Matched
+// reports whether it already had an opponent.
 func matchDTOFrom(r lobby.EnqueueResult) matchDTO {
-	if !r.Matched {
-		return matchDTO{Matched: false}
-	}
 	g := gameDTOFromGame(r.Game)
-	return matchDTO{Matched: true, Game: &g}
+	return matchDTO{Matched: r.Matched, Game: &g}
 }
 
 // chatDTOFrom projects a chat message into its DTO.