Stage 3: game domain (lifecycle, journal+cache, hint, word-check, GCG, stats)

internal/game drives the engine over a single match and owns everything the
engine does not: event-sourced persistence (a games row + an append-only decoded
move journal, with the live engine.Game kept warm in a cache and rebuilt by
replay on a miss), the play/pass/exchange/resign transitions with
validate-at-submit scoring, an unlimited score/legality preview, the hint
(per-game allowance + profile wallet), the word-check tool with complaint
capture, per-player game state, history and GCG export (Poslfit dialect), and a
background turn-timeout sweeper that auto-resigns overdue turns honouring each
player's daily away window. Like Stages 1-2 it is a service/store layer with no
HTTP; the gateway surface lands in Stage 6.

Engine: additive decoded domain API (Direction, SubmitPlay/SubmitExchange/
EvaluatePlay/HintView/Hand, MoveRecord.{Dir,MainRow,MainCol}, Registry.Lookup,
ParseVariant) so internal/game never imports scrabble-solver; and a Resign fix
so the resigner keeps their score yet never wins (the other player wins a
two-player game). Timeout reuses Resign.

Persistence: migration 00002 adds games, game_players, game_moves, complaints,
account_stats and extends accounts with away_start/away_end/hint_balance; go-jet
regenerated. account gained SpendHint. Config adds BACKEND_DICT_DIR (required),
BACKEND_DICT_VERSION, BACKEND_GAME_TIMEOUT_SWEEP_INTERVAL, BACKEND_GAME_CACHE_TTL;
main loads the registry at boot (hard dependency) and starts the sweeper.

Tests: engine resign + decoded-API tests; game unit tests (GCG, away-window
boundaries, hint budget, cache, keyed mutex, payload); inttest integration
(lifecycle, replay equivalence, timeout sweep with away grace, resign stats,
hint policy, word-check/complaint, per-game-lock). Docs (PLAN, ARCHITECTURE,
FUNCTIONAL +_ru, TESTING, README) updated.

backend/internal/account/account.go

@@ -33,12 +33,19 @@ const uniqueViolation = "23505"
 // ErrNotFound is returned when no account matches the lookup.
 var ErrNotFound = errors.New("account: not found")
 
-// Account is a durable internal account.
+// Account is a durable internal account. AwayStart and AwayEnd bound the daily
+// local-time window (in TimeZone) during which the player is asleep: the
+// turn-timeout sweeper does not auto-resign them inside it, and the robot reuses
+// it for its own sleep in a later stage. HintBalance is the player's wallet of
+// purchasable hints, spent after a game's per-seat allowance.
 type Account struct {
 	ID                  uuid.UUID
 	DisplayName         string
 	PreferredLanguage   string
 	TimeZone            string
+	AwayStart           time.Time
+	AwayEnd             time.Time
+	HintBalance         int
 	BlockChat           bool
 	BlockFriendRequests bool
 	CreatedAt           time.Time
@@ -165,6 +172,28 @@ func (s *Store) create(ctx context.Context, kind, externalID string) (Account, e
 	return created, nil
 }
 
+// SpendHint atomically decrements the account's hint wallet by one, returning
+// true when a hint was spent and false when the balance was already empty. The
+// guarded UPDATE keeps it safe under concurrent spends across the player's games.
+func (s *Store) SpendHint(ctx context.Context, id uuid.UUID) (bool, error) {
+	stmt := table.Accounts.
+		UPDATE(table.Accounts.HintBalance, table.Accounts.UpdatedAt).
+		SET(table.Accounts.HintBalance.SUB(postgres.Int(1)), postgres.TimestampzT(time.Now().UTC())).
+		WHERE(
+			table.Accounts.AccountID.EQ(postgres.UUID(id)).
+				AND(table.Accounts.HintBalance.GT(postgres.Int(0))),
+		)
+	res, err := stmt.ExecContext(ctx, s.db)
+	if err != nil {
+		return false, fmt.Errorf("account: spend hint %s: %w", id, err)
+	}
+	n, err := res.RowsAffected()
+	if err != nil {
+		return false, fmt.Errorf("account: spend hint rows %s: %w", id, err)
+	}
+	return n > 0, nil
+}
+
 // modelToAccount projects a generated model row into the public Account struct.
 func modelToAccount(row model.Accounts) Account {
 	return Account{
@@ -172,6 +201,9 @@ func modelToAccount(row model.Accounts) Account {
 		DisplayName:         row.DisplayName,
 		PreferredLanguage:   row.PreferredLanguage,
 		TimeZone:            row.TimeZone,
+		AwayStart:           row.AwayStart,
+		AwayEnd:             row.AwayEnd,
+		HintBalance:         int(row.HintBalance),
 		BlockChat:           row.BlockChat,
 		BlockFriendRequests: row.BlockFriendRequests,
 		CreatedAt:           row.CreatedAt,