Stage 17 round 5 (L2): robot play-to-win intent + next-move ETA in the admin game card

The admin game detail now shows, per robot seat, the game's deterministic play-to-win
decision (from the bag seed) and — while it is that robot's turn — its scheduled next-move
ETA (sampled think-time delay, deferred past the sleep window), plus a caption with the
~40% global target. Wiring: robot.PlayToWin/NextMoveAt/PlayToWinTargetPercent exports,
account.IsRobot, game RobotSchedule (seed + turn-start). Tests: NextMoveAt invariants
(never early, never in the sleep window), PlayToWin export, and an admin render integration
test asserting the intent + ETA + target appear.

backend/internal/account/userlist.go

@@ -34,6 +34,19 @@ type UserFilter struct {
 // robotExists is the correlated subquery testing whether account a is a robot.
 const robotExists = `EXISTS (SELECT 1 FROM backend.identities i WHERE i.account_id = a.account_id AND i.kind = 'robot')`
 
+// IsRobot reports whether the account is a robot pool member (it carries a robot
+// identity). The admin console uses it to label a game's robot seats.
+func (s *Store) IsRobot(ctx context.Context, accountID uuid.UUID) (bool, error) {
+	var ok bool
+	err := s.db.QueryRowContext(ctx,
+		`SELECT EXISTS (SELECT 1 FROM backend.identities WHERE account_id = $1 AND kind = 'robot')`,
+		accountID).Scan(&ok)
+	if err != nil {
+		return false, fmt.Errorf("account: is-robot %s: %w", accountID, err)
+	}
+	return ok, nil
+}
+
 // userListWhere builds the shared WHERE clause and its positional args (from $1).
 func userListWhere(f UserFilter) (string, []any) {
 	args := []any{f.Robots}