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/merge_test.go

@@ -30,6 +30,34 @@ func setStats(t *testing.T, id uuid.UUID, w, l, d, mg, mw int) {
 	}
 }
 
+func setStatsCounts(t *testing.T, id uuid.UUID, moves, hints int) {
+	t.Helper()
+	if _, err := testDB.ExecContext(context.Background(),
+		`UPDATE backend.account_stats SET moves=$2, hints_used=$3 WHERE account_id=$1`, id, moves, hints); err != nil {
+		t.Fatalf("set stats counts: %v", err)
+	}
+}
+
+func setBestMove(t *testing.T, id uuid.UUID, variant string, score int) {
+	t.Helper()
+	tiles := `[{"letter":"c","value":3,"blank":false}]`
+	if _, err := testDB.ExecContext(context.Background(),
+		`INSERT INTO backend.account_best_move (account_id, variant, score, tiles) VALUES ($1,$2,$3,$4)
+		 ON CONFLICT (account_id, variant) DO UPDATE SET score=$3, tiles=$4`, id, variant, score, tiles); err != nil {
+		t.Fatalf("set best move: %v", err)
+	}
+}
+
+func bestMoveCount(t *testing.T, id uuid.UUID) int {
+	t.Helper()
+	var n int
+	if err := testDB.QueryRowContext(context.Background(),
+		`SELECT count(*) FROM backend.account_best_move WHERE account_id=$1`, id).Scan(&n); err != nil {
+		t.Fatalf("best move count: %v", err)
+	}
+	return n
+}
+
 func setWallet(t *testing.T, id uuid.UUID, hints int, paid bool) {
 	t.Helper()
 	if _, err := testDB.ExecContext(context.Background(),
@@ -110,8 +138,15 @@ func TestAccountMergeCore(t *testing.T) {
 
 	setStats(t, primary, 1, 0, 0, 100, 90)
 	setStats(t, secondary, 3, 1, 2, 400, 80)
+	setStatsCounts(t, primary, 100, 5)
+	setStatsCounts(t, secondary, 50, 8)
 	setWallet(t, primary, 2, false)
 	setWallet(t, secondary, 5, true)
+	// Best moves: secondary's scrabble_en (80) beats primary's (50) and is kept; secondary's
+	// scrabble_ru (30) is new to primary and carried over.
+	setBestMove(t, primary, "scrabble_en", 50)
+	setBestMove(t, secondary, "scrabble_en", 80)
+	setBestMove(t, secondary, "scrabble_ru", 30)
 
 	email := "merge-" + uuid.NewString() + "@example.com"
 	bindEmailIdentity(t, secondary, email)
@@ -153,6 +188,26 @@ func TestAccountMergeCore(t *testing.T) {
 	if mergedInto(t, secondary) != primary {
 		t.Errorf("secondary.merged_into = %s, want primary %s", mergedInto(t, secondary), primary)
 	}
+
+	// The moves/hints counters sum, and the per-variant best moves merge (the higher score
+	// per variant kept), with the secondary's best-move rows cleaned up.
+	st, err := store.GetStats(ctx, primary)
+	if err != nil {
+		t.Fatalf("get merged stats: %v", err)
+	}
+	if st.Moves != 150 || st.HintsUsed != 13 {
+		t.Errorf("primary moves/hints = %d/%d, want 150/13", st.Moves, st.HintsUsed)
+	}
+	best := map[string]int{}
+	for _, b := range st.BestMoves {
+		best[b.Variant] = b.Score
+	}
+	if len(st.BestMoves) != 2 || best["scrabble_en"] != 80 || best["scrabble_ru"] != 30 {
+		t.Errorf("primary best moves = %+v, want scrabble_en:80 + scrabble_ru:30", st.BestMoves)
+	}
+	if bestMoveCount(t, secondary) != 0 {
+		t.Error("secondary best-move rows should be deleted after merge")
+	}
 }
 
 // TestAccountMergeActiveGameConflict refuses a merge when the two share an active