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/account/stats.go

@@ -2,6 +2,7 @@ package account
 
 import (
 	"context"
+	"encoding/json"
 	"errors"
 	"fmt"
 
@@ -13,16 +14,43 @@ import (
 	"scrabble/backend/internal/postgres/jet/backend/table"
 )
 
+// BestMoveTile is one letter cell of a best-move word: its concrete letter (the
+// designated letter for a blank), its tile point value (0 for a blank) and whether it
+// is a blank. It is the persisted/served shape: the game domain marshals a slice of
+// these into account_best_move.tiles, and the statistics screen renders them as game
+// tiles without consulting the variant's alphabet.
+type BestMoveTile struct {
+	Letter string `json:"letter"`
+	Value  int    `json:"value"`
+	Blank  bool   `json:"blank"`
+}
+
+// BestMove is an account's highest-scoring single play within one game variant: the
+// move's total score (every word it formed plus the all-tiles bonus, matching
+// MaxWordPoints) and its main word as an ordered slice of tiles.
+type BestMove struct {
+	Variant string
+	Score   int
+	Tiles   []BestMoveTile
+}
+
 // Stats is a durable account's lifetime record, written by the game domain on each
 // finish and read for the player's statistics screen. MaxGamePoints is the best
 // single game's total; MaxWordPoints is the best single move's score (which already
-// includes every word it formed plus the all-tiles bonus).
+// includes every word it formed plus the all-tiles bonus). BestMoves holds the same
+// best move broken down per variant, with the word itself — empty for an account with
+// no recorded play yet, and never carrying a variant the account has not played.
 type Stats struct {
 	Wins          int
 	Losses        int
 	Draws         int
 	MaxGamePoints int
 	MaxWordPoints int
+	// Moves is the lifetime count of the account's plays (tile placements); HintsUsed is the
+	// lifetime count of hints taken. The statistics screen shows the hint share (HintsUsed / Moves).
+	Moves     int
+	HintsUsed int
+	BestMoves []BestMove
 }
 
 // GetStats returns the lifetime statistics for id. An account with no account_stats
@@ -40,11 +68,48 @@ func (s *Store) GetStats(ctx context.Context, id uuid.UUID) (Stats, error) {
 		}
 		return Stats{}, fmt.Errorf("account: get stats %s: %w", id, err)
 	}
+	best, err := s.bestMoves(ctx, id)
+	if err != nil {
+		return Stats{}, err
+	}
 	return Stats{
 		Wins:          int(row.Wins),
 		Losses:        int(row.Losses),
 		Draws:         int(row.Draws),
 		MaxGamePoints: int(row.MaxGamePoints),
 		MaxWordPoints: int(row.MaxWordPoints),
+		Moves:         int(row.Moves),
+		HintsUsed:     int(row.HintsUsed),
+		BestMoves:     best,
 	}, nil
 }
+
+// bestMoves reads an account's per-variant best moves, ordered by variant for a stable
+// response. Each row's tiles JSON is decoded into the served BestMoveTile slice. An
+// account with no recorded play yields an empty (nil) slice rather than an error.
+func (s *Store) bestMoves(ctx context.Context, id uuid.UUID) ([]BestMove, error) {
+	stmt := postgres.SELECT(
+		table.AccountBestMove.Variant,
+		table.AccountBestMove.Score,
+		table.AccountBestMove.Tiles,
+	).
+		FROM(table.AccountBestMove).
+		WHERE(table.AccountBestMove.AccountID.EQ(postgres.UUID(id))).
+		ORDER_BY(table.AccountBestMove.Variant.ASC())
+	var rows []model.AccountBestMove
+	if err := stmt.QueryContext(ctx, s.db, &rows); err != nil {
+		if errors.Is(err, qrm.ErrNoRows) {
+			return nil, nil
+		}
+		return nil, fmt.Errorf("account: best moves %s: %w", id, err)
+	}
+	out := make([]BestMove, 0, len(rows))
+	for _, r := range rows {
+		var tiles []BestMoveTile
+		if err := json.Unmarshal([]byte(r.Tiles), &tiles); err != nil {
+			return nil, fmt.Errorf("account: decode best-move tiles %s/%s: %w", id, r.Variant, err)
+		}
+		out = append(out, BestMove{Variant: r.Variant, Score: int(r.Score), Tiles: tiles})
+	}
+	return out, nil
+}