feat(stats): per-game hints used + lifetime moves and hint share

Store the hints a player used in each game, and add two lifetime tiles —
Moves and Hint share — to the statistics screen.

- per-game: game_players.hints_used now counts EVERY hint (allowance + wallet),
  not just the free allowance, so it is the seat's true total hints used this
  game. The allowance decision (used < HintsPerPlayer) and the hint badge values
  (hints_remaining / wallet_balance) are unchanged — the lobby hint-count fix does
  NOT regress; only the admin "hints used" column, which silently under-counted
  wallet hints, becomes accurate.
- account_stats gains two summed counters: moves (the player's plays — passes and
  exchanges excluded) and hints_used (every hint). Computed at game finish in
  buildStats over the same non-guest, non-honest-AI games as the rest of the stats.
- wire: StatsView gains moves + hints_used (trailing); gateway + UI codec + model;
  regen.
- ui: two tiles (Moves, Hint share = hints_used/moves, one-decimal % in the active
  locale); card order games·wins·draws·losses·moves·hint-share·best game·win-rate.
- docs: ARCHITECTURE §9 + baseline comment, FUNCTIONAL (+ru), UI_DESIGN.

Tests: TestHintPolicy (hints_used counts the wallet hint), TestGameLifecycleAndStats
(moves>0, hints=0), gateway stats round-trip, UI hintShare unit + codec + e2e.

backend/internal/game/service.go

@@ -1027,12 +1027,7 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 	}
 
 	walletAfter := acc.HintBalance
-	if fromAllowance {
-		if err := svc.store.SpendHintAllowance(ctx, gameID, seat); err != nil {
-			return HintResult{}, err
-		}
-		used++
-	} else {
+	if !fromAllowance {
 		spent, err := svc.accounts.SpendHint(ctx, accountID)
 		if err != nil {
 			return HintResult{}, err
@@ -1042,6 +1037,13 @@ func (svc *Service) Hint(ctx context.Context, gameID, accountID uuid.UUID) (Hint
 		}
 		walletAfter--
 	}
+	// hints_used is the per-game total (allowance + wallet): every hint increments it. The first
+	// HintsPerPlayer hints are the free allowance (so fromAllowance above stays correct); the rest
+	// are charged to the wallet. Counting all hints feeds the player's lifetime hint statistics.
+	if err := svc.store.IncHintsUsed(ctx, gameID, seat); err != nil {
+		return HintResult{}, err
+	}
+	used++
 	return HintResult{Move: move, HintsRemaining: hintsRemaining(pre.HintsPerPlayer, used, walletAfter), WalletBalance: walletAfter}, nil
 }
 
@@ -1429,10 +1431,12 @@ func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	res := g.Result()
 	bestRec := make(map[int]engine.MoveRecord)
 	blanks := make(map[[2]int]bool)
+	plays := make(map[int]int) // per player: count of plays (tile placements), for the "moves" stat
 	for _, rec := range g.Log() {
 		if rec.Action != engine.ActionPlay {
 			continue
 		}
+		plays[rec.Player]++
 		for _, t := range rec.Tiles {
 			if t.Blank {
 				blanks[[2]int{t.Row, t.Col}] = true
@@ -1446,7 +1450,9 @@ func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	values := letterValues(g.Variant())
 	out := make([]statDelta, 0, len(seats))
 	for _, s := range seats {
-		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat)}
+		// moves counts the seat's plays; hintsUsed is the seat's total hints this game. Both are
+		// summed into account_stats so the screen can show the hint share (hints_used / moves).
+		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat), moves: plays[s.Seat], hintsUsed: s.HintsUsed}
 		if rec, ok := bestRec[s.Seat]; ok {
 			d.wordPoints = rec.Score
 			if rec.Score > 0 {