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/inttest/game_test.go

@@ -150,6 +150,14 @@ func TestGameLifecycleAndStats(t *testing.T) {
 		if err != nil {
 			t.Fatalf("get stats: %v", err)
 		}
+		// The player made at least one scoring play (maxWord > 0), so the moves aggregate is
+		// positive; no hints were taken in this greedy game, so the hints aggregate stays 0.
+		if st.Moves <= 0 {
+			t.Errorf("moves = %d, want > 0", st.Moves)
+		}
+		if st.HintsUsed != 0 {
+			t.Errorf("hints used = %d, want 0 (no hints taken)", st.HintsUsed)
+		}
 		if len(st.BestMoves) != 1 {
 			t.Fatalf("want one best move (only scrabble_en played), got %d: %+v", len(st.BestMoves), st.BestMoves)
 		}
@@ -429,6 +437,15 @@ func TestHintPolicy(t *testing.T) {
 	if res.HintsRemaining != 1 || res.WalletBalance != 1 {
 		t.Errorf("wallet hint: hints=%d wallet=%d, want 1/1", res.HintsRemaining, res.WalletBalance)
 	}
+	// game_players.hints_used counts BOTH hints (1 allowance + 1 wallet) — the per-game total
+	// that feeds the player's lifetime hint statistics, not just the allowance.
+	st2, err := svc.GameState(ctx, g.ID, seats[0])
+	if err != nil {
+		t.Fatalf("state after wallet hint: %v", err)
+	}
+	if got := st2.Game.Seats[0].HintsUsed; got != 2 {
+		t.Errorf("hints_used = %d after allowance + wallet hint, want 2", got)
+	}
 
 	off, err := svc.Create(ctx, game.CreateParams{
 		Variant: engine.VariantEnglish, Seats: seats, TurnTimeout: 24 * time.Hour,