feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

backend/internal/inttest/game_test.go

@@ -11,6 +11,7 @@ import (
 
 	"github.com/google/uuid"
 
+	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/game"
 )
@@ -120,8 +121,8 @@ func TestGameLifecycleAndStats(t *testing.T) {
 		t.Fatalf("final game not finished: %+v", last.Game)
 	}
 
-	w0, l0, d0, mg0, _, ok0 := readStats(t, seats[0])
-	w1, l1, d1, mg1, _, ok1 := readStats(t, seats[1])
+	w0, l0, d0, mg0, mw0, ok0 := readStats(t, seats[0])
+	w1, l1, d1, mg1, mw1, ok1 := readStats(t, seats[1])
 	if !ok0 || !ok1 {
 		t.Fatal("both players must have a stats row")
 	}
@@ -133,6 +134,52 @@ func TestGameLifecycleAndStats(t *testing.T) {
 	if !decisive && !draw {
 		t.Errorf("inconsistent W/L/D: p0(%d/%d/%d) p1(%d/%d/%d)", w0, l0, d0, w1, l1, d1)
 	}
+
+	// Each player who made a scoring play gets exactly one per-variant best move (only
+	// scrabble_en was played here); its score equals the aggregate max_word_points and it
+	// carries the decoded word as tiles.
+	accounts := account.NewStore(testDB)
+	for _, p := range []struct {
+		id      uuid.UUID
+		maxWord int
+	}{{seats[0], mw0}, {seats[1], mw1}} {
+		if p.maxWord == 0 {
+			continue // a player who only passed has no best move
+		}
+		st, err := accounts.GetStats(ctx, p.id)
+		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)
+		}
+		bm := st.BestMoves[0]
+		if bm.Variant != engine.VariantEnglish.String() {
+			t.Errorf("best move variant = %q, want %q", bm.Variant, engine.VariantEnglish.String())
+		}
+		if bm.Score != p.maxWord {
+			t.Errorf("best move score %d != max_word_points %d", bm.Score, p.maxWord)
+		}
+		if len(bm.Tiles) == 0 {
+			t.Error("best move word is empty")
+		}
+		for _, tl := range bm.Tiles {
+			if tl.Letter == "" {
+				t.Error("best move tile has empty letter")
+			}
+			if tl.Blank && tl.Value != 0 {
+				t.Errorf("blank tile must score 0, got %d", tl.Value)
+			}
+		}
+	}
 }
 
 // TestReplayEquivalence plays a few moves through one service, then proves a
@@ -369,6 +416,15 @@ func TestHintPolicy(t *testing.T) {
 	if _, err := svc.Hint(ctx, g.ID, seats[0]); err != nil { // spends the allowance
 		t.Fatalf("first hint: %v", err)
 	}
+	// The allowance is spent before the wallet: with an empty wallet, the state now reports no
+	// hints left and a zero wallet, so the per-game allowance (HintsRemaining-WalletBalance) is 0.
+	st, err := svc.GameState(ctx, g.ID, seats[0])
+	if err != nil {
+		t.Fatalf("state: %v", err)
+	}
+	if st.HintsRemaining != 0 || st.WalletBalance != 0 {
+		t.Errorf("after allowance hint: hints=%d wallet=%d, want 0/0", st.HintsRemaining, st.WalletBalance)
+	}
 	if _, err := svc.Hint(ctx, g.ID, seats[0]); !errors.Is(err, game.ErrNoHintsLeft) {
 		t.Fatalf("second hint = %v, want ErrNoHintsLeft", err)
 	}
@@ -377,8 +433,18 @@ func TestHintPolicy(t *testing.T) {
 	if err != nil {
 		t.Fatalf("wallet hint: %v", err)
 	}
-	if res.HintsRemaining != 1 {
-		t.Errorf("hints remaining = %d, want 1", res.HintsRemaining)
+	// The allowance stays exhausted; the wallet dropped 2->1, and WalletBalance carries it alone.
+	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{