feat: honest AI opponent in quick game

New Game's quick game gains an explicit opponent selector — 🤖 AI (default)
or 👤 Random player. AI starts a game seated with a pooled robot that joins
and moves at once: no per-move timeout (a 7-day inactivity loss reusing the
turn-timeout sweeper), chat/nudge disabled, no statistics, the opponent shown
as 🤖 everywhere. The random path (disguised robot) is unchanged.

Driven by one game flag (games.vs_ai), set only on AI-started games so the
disguised path is never revealed; Matchmaker.StartVsAI seats the robot
directly (no open pool); the robot replies event-driven via the game service's
after-commit/after-create hook. Wire: vs_ai on EnqueueRequest + GameView.

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

@@ -32,4 +32,5 @@ type Games struct {
 	OpenDeadlineAt       *time.Time
 	DropoutTiles         string
 	MultipleWordsPerTurn bool
+	VsAi                 bool
 }

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

@@ -36,6 +36,7 @@ type gamesTable struct {
 	OpenDeadlineAt       postgres.ColumnTimestampz
 	DropoutTiles         postgres.ColumnString
 	MultipleWordsPerTurn postgres.ColumnBool
+	VsAi                 postgres.ColumnBool
 
 	AllColumns     postgres.ColumnList
 	MutableColumns postgres.ColumnList
@@ -96,9 +97,10 @@ func newGamesTableImpl(schemaName, tableName, alias string) gamesTable {
 		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, 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}
+		VsAiColumn                 = postgres.BoolColumn("vs_ai")
+		allColumns                 = postgres.ColumnList{GameIDColumn, VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, OpenDeadlineAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn, VsAiColumn}
+		mutableColumns             = postgres.ColumnList{VariantColumn, DictVersionColumn, SeedColumn, StatusColumn, PlayersColumn, ToMoveColumn, TurnStartedAtColumn, TurnTimeoutSecsColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, EndReasonColumn, CreatedAtColumn, UpdatedAtColumn, FinishedAtColumn, OpenDeadlineAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn, VsAiColumn}
+		defaultColumns             = postgres.ColumnList{StatusColumn, ToMoveColumn, TurnStartedAtColumn, HintsAllowedColumn, HintsPerPlayerColumn, MoveCountColumn, CreatedAtColumn, UpdatedAtColumn, DropoutTilesColumn, MultipleWordsPerTurnColumn, VsAiColumn}
 	)
 
 	return gamesTable{
@@ -124,6 +126,7 @@ func newGamesTableImpl(schemaName, tableName, alias string) gamesTable {
 		OpenDeadlineAt:       OpenDeadlineAtColumn,
 		DropoutTiles:         DropoutTilesColumn,
 		MultipleWordsPerTurn: MultipleWordsPerTurnColumn,
+		VsAi:                 VsAiColumn,
 
 		AllColumns:     allColumns,
 		MutableColumns: mutableColumns,