feat(stats): show the best move word per game variant

Replace the single "best move" number on the statistics screen with a
full-width per-variant breakdown: the highest-scoring play in each variant
the player has played, drawn as game tiles (a wildcard shows its letter but
no value), with the words and scores right-aligned to shared edges.

- backend: new account_best_move table (PK account_id+variant) keeping the
  main word as JSON tiles {letter,value,blank}; captured at game finish in
  buildStats (blank flags taken from every placed blank — equivalent to the
  final board), upserted in the finish transaction and replaced only by a
  strictly higher-scoring play. Guest/honest-AI games still record nothing.
  GetStats + statsDTO expose best_moves.
- wire: StatsView gains best_moves:[BestMoveView{variant,score,word:[BestMoveTile]}]
  (trailing, backward-compatible); gateway encodeStats + UI codec updated.
- ui: new WordTiles component (board's tile look, fixed px size); Stats.svelte
  drops the maxWord card and adds the full-width best-move card (catalogue
  order, empty variants omitted).
- docs: ARCHITECTURE §9 + schema, FUNCTIONAL (+ru), UI_DESIGN.

Tests: mainWordTiles unit + buildStats end-to-end (inttest) + gateway and UI
codec round-trips (incl. a blank tile) + e2e.

backend/internal/game/service.go

@@ -1419,19 +1419,41 @@ func replayMove(g *engine.Game, mv HistoryMove) error {
 }
 
 // buildStats derives each seat's statistics contribution from a finished game:
-// win/loss/draw from the (resignation-aware) winner, the final score, and the
-// best single-move score from the log.
+// win/loss/draw from the (resignation-aware) winner, the final score, and the best
+// single play from the log — its score and, for the per-variant breakdown, its main
+// word as rendering tiles. Blank flags are taken from every blank ever placed (so a
+// blank laid by an earlier move and embedded in the best word is honoured), which is
+// equivalent to reading the final board since a placed tile never moves.
 func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	res := g.Result()
-	best := make(map[int]int)
+	bestRec := make(map[int]engine.MoveRecord)
+	blanks := make(map[[2]int]bool)
 	for _, rec := range g.Log() {
-		if rec.Action == engine.ActionPlay && rec.Score > best[rec.Player] {
-			best[rec.Player] = rec.Score
+		if rec.Action != engine.ActionPlay {
+			continue
+		}
+		for _, t := range rec.Tiles {
+			if t.Blank {
+				blanks[[2]int{t.Row, t.Col}] = true
+			}
+		}
+		if cur, ok := bestRec[rec.Player]; !ok || rec.Score > cur.Score {
+			bestRec[rec.Player] = rec
 		}
 	}
+	variant := g.Variant().String()
+	values := letterValues(g.Variant())
 	out := make([]statDelta, 0, len(seats))
 	for _, s := range seats {
-		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat), wordPoints: best[s.Seat]}
+		d := statDelta{accountID: s.AccountID, gamePoints: g.Score(s.Seat)}
+		if rec, ok := bestRec[s.Seat]; ok {
+			d.wordPoints = rec.Score
+			if rec.Score > 0 {
+				d.bestVariant = variant
+				d.bestScore = rec.Score
+				d.bestTiles = mainWordTiles(rec, blanks, values)
+			}
+		}
 		switch {
 		case res.Winner < 0:
 			d.draws = 1
@@ -1445,6 +1467,49 @@ func buildStats(g *engine.Game, seats []Seat) []statDelta {
 	return out
 }
 
+// letterValues builds a lower-cased letter -> tile value lookup for a variant from the
+// engine's alphabet table, so a best-move word can be rendered with per-tile values on a
+// screen (statistics) that has not cached the variant's alphabet. It is empty for an
+// unrecognised variant, leaving every value zero.
+func letterValues(v engine.Variant) map[string]int {
+	table, err := engine.AlphabetTable(v)
+	if err != nil {
+		return nil
+	}
+	m := make(map[string]int, len(table))
+	for _, e := range table {
+		m[strings.ToLower(e.Letter)] = e.Value
+	}
+	return m
+}
+
+// mainWordTiles decodes a play's main word into rendering tiles: each letter with its
+// tile value (0 for a blank) and blank flag. blanks is the set of board coordinates a
+// blank was ever placed on; values maps a lower-cased letter to its tile value. It walks
+// the word from its first-letter coordinate along the play's orientation.
+func mainWordTiles(rec engine.MoveRecord, blanks map[[2]int]bool, values map[string]int) []account.BestMoveTile {
+	if len(rec.Words) == 0 {
+		return nil
+	}
+	dr, dc := 0, 1
+	if rec.Dir == engine.Vertical {
+		dr, dc = 1, 0
+	}
+	letters := []rune(rec.Words[0])
+	out := make([]account.BestMoveTile, len(letters))
+	for i, r := range letters {
+		row, col := rec.MainRow+i*dr, rec.MainCol+i*dc
+		blank := blanks[[2]int{row, col}]
+		letter := string(r)
+		value := 0
+		if !blank {
+			value = values[strings.ToLower(letter)]
+		}
+		out[i] = account.BestMoveTile{Letter: letter, Value: value, Blank: blank}
+	}
+	return out
+}
+
 // nonGuestSeats filters out guest seats so the finish-time statistics are
 // recomputed for durable non-guest accounts only — guests never accrue
 // statistics (docs/ARCHITECTURE.md §9). It is called once per game, on finish.