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/config/config.go

@@ -8,6 +8,7 @@ import (
 	"strconv"
 	"time"
 
+	"scrabble/backend/internal/game"
 	"scrabble/backend/internal/postgres"
 	"scrabble/backend/internal/telemetry"
 )
@@ -22,6 +23,8 @@ type Config struct {
 	Postgres postgres.Config
 	// Telemetry configures the OpenTelemetry providers.
 	Telemetry telemetry.Config
+	// Game configures the game subsystem (dictionaries, sweeper, live-game cache).
+	Game game.Config
 }
 
 // Defaults applied when the corresponding environment variable is unset.
@@ -54,11 +57,22 @@ func Load() (Config, error) {
 	tel.TracesExporter = envOr("BACKEND_OTEL_TRACES_EXPORTER", tel.TracesExporter)
 	tel.MetricsExporter = envOr("BACKEND_OTEL_METRICS_EXPORTER", tel.MetricsExporter)
 
+	gm := game.DefaultConfig()
+	gm.DictDir = envOr("BACKEND_DICT_DIR", gm.DictDir)
+	gm.DictVersion = envOr("BACKEND_DICT_VERSION", gm.DictVersion)
+	if gm.TimeoutSweepInterval, err = envDuration("BACKEND_GAME_TIMEOUT_SWEEP_INTERVAL", gm.TimeoutSweepInterval); err != nil {
+		return Config{}, err
+	}
+	if gm.CacheTTL, err = envDuration("BACKEND_GAME_CACHE_TTL", gm.CacheTTL); err != nil {
+		return Config{}, err
+	}
+
 	c := Config{
 		HTTPAddr:  envOr("BACKEND_HTTP_ADDR", defaultHTTPAddr),
 		LogLevel:  envOr("BACKEND_LOG_LEVEL", defaultLogLevel),
 		Postgres:  pg,
 		Telemetry: tel,
+		Game:      gm,
 	}
 	if err := c.validate(); err != nil {
 		return Config{}, err
@@ -82,6 +96,9 @@ func (c Config) validate() error {
 	if err := c.Telemetry.Validate(); err != nil {
 		return fmt.Errorf("config: %w", err)
 	}
+	if err := c.Game.Validate(); err != nil {
+		return fmt.Errorf("config: %w (set BACKEND_DICT_DIR)", err)
+	}
 	return nil
 }