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/jet/backend/model/game_players.go

@@ -14,7 +14,7 @@ import (
 type GamePlayers struct {
 	GameID    uuid.UUID `sql:"primary_key"`
 	Seat      int16     `sql:"primary_key"`
-	AccountID uuid.UUID
+	AccountID *uuid.UUID
 	Score     int32
 	HintsUsed int16
 	IsWinner  bool

backend/internal/postgres/jet/backend/model/games.go

@@ -29,6 +29,7 @@ type Games struct {
 	CreatedAt            time.Time
 	UpdatedAt            time.Time
 	FinishedAt           *time.Time
+	OpenDeadlineAt       *time.Time
 	DropoutTiles         string
 	MultipleWordsPerTurn bool
 }

backend/internal/postgres/jet/backend/table/games.go

@@ -33,6 +33,7 @@ type gamesTable struct {
 	CreatedAt            postgres.ColumnTimestampz
 	UpdatedAt            postgres.ColumnTimestampz
 	FinishedAt           postgres.ColumnTimestampz
+	OpenDeadlineAt       postgres.ColumnTimestampz
 	DropoutTiles         postgres.ColumnString
 	MultipleWordsPerTurn postgres.ColumnBool
 
@@ -92,10 +93,11 @@ func newGamesTableImpl(schemaName, tableName, alias string) gamesTable {
 		CreatedAtColumn            = postgres.TimestampzColumn("created_at")
 		UpdatedAtColumn            = postgres.TimestampzColumn("updated_at")
 		FinishedAtColumn           = postgres.TimestampzColumn("finished_at")
+		OpenDeadlineAtColumn       = postgres.TimestampzColumn("open_deadline_at")
 		DropoutTilesColumn         = postgres.StringColumn("dropout_tiles")
 		MultipleWordsPerTurnColumn = postgres.BoolColumn("multiple_words_per_turn")
-		allColumns                 = postgres.ColumnList{GameIDColumn, VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn}
-		mutableColumns             = postgres.ColumnList{VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn}
+		allColumns                 = postgres.ColumnList{GameIDColumn, VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, OpenDeadlineAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn}
+		mutableColumns             = postgres.ColumnList{VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, OpenDeadlineAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn}
 		defaultColumns             = postgres.ColumnList{StatusColumn, ToMoveColumn, TurnStartedAtColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, CreatedAtColumn, UpdatedAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn}
 	)
 
@@ -119,6 +121,7 @@ func newGamesTableImpl(schemaName, tableName, alias string) gamesTable {
 		CreatedAt:            CreatedAtColumn,
 		UpdatedAt:            UpdatedAtColumn,
 		FinishedAt:           FinishedAtColumn,
+		OpenDeadlineAt:       OpenDeadlineAtColumn,
 		DropoutTiles:         DropoutTilesColumn,
 		MultipleWordsPerTurn: MultipleWordsPerTurnColumn,