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/server/handlers_account.go

@@ -29,13 +29,27 @@ type updateProfileRequest struct {
 }
 
 // statsDTO is a durable account's lifetime statistics (the derived games-played and
-// win-rate are computed client-side).
+// win-rate are computed client-side). BestMoves breaks the best move down per variant,
+// carrying the word itself; it is absent for an account with no recorded play and never
+// lists a variant the account has not played.
 type statsDTO struct {
-	Wins          int `json:"wins"`
-	Losses        int `json:"losses"`
-	Draws         int `json:"draws"`
-	MaxGamePoints int `json:"max_game_points"`
-	MaxWordPoints int `json:"max_word_points"`
+	Wins          int           `json:"wins"`
+	Losses        int           `json:"losses"`
+	Draws         int           `json:"draws"`
+	MaxGamePoints int           `json:"max_game_points"`
+	MaxWordPoints int           `json:"max_word_points"`
+	Moves         int           `json:"moves"`
+	HintsUsed     int           `json:"hints_used"`
+	BestMoves     []bestMoveDTO `json:"best_moves,omitempty"`
+}
+
+// bestMoveDTO is one variant's best play: the variant label, the play's total score and
+// its main word as ordered tiles (letter, value, blank — value 0 for a blank), so the
+// client renders it as game tiles without the variant's alphabet table.
+type bestMoveDTO struct {
+	Variant string                 `json:"variant"`
+	Score   int                    `json:"score"`
+	Word    []account.BestMoveTile `json:"word"`
 }
 
 // parseAwayTime parses an "HH:MM" away-window bound.
@@ -140,11 +154,21 @@ func (s *Server) handleStats(c *gin.Context) {
 		s.abortErr(c, err)
 		return
 	}
+	var best []bestMoveDTO
+	if len(st.BestMoves) > 0 {
+		best = make([]bestMoveDTO, len(st.BestMoves))
+		for i, b := range st.BestMoves {
+			best[i] = bestMoveDTO{Variant: b.Variant, Score: b.Score, Word: b.Tiles}
+		}
+	}
 	c.JSON(http.StatusOK, statsDTO{
 		Wins:          st.Wins,
 		Losses:        st.Losses,
 		Draws:         st.Draws,
 		MaxGamePoints: st.MaxGamePoints,
 		MaxWordPoints: st.MaxWordPoints,
+		Moves:         st.Moves,
+		HintsUsed:     st.HintsUsed,
+		BestMoves:     best,
 	})
 }