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.

docs/ARCHITECTURE.md

@@ -568,7 +568,8 @@ disguised robot stays indistinguishable from a person.
   the `kind` admitting `robot`),
   `sessions` (revoke-only opaque-token hashes), the game tables
   `games` (carrying the `dropout_tiles` disposition column), `game_players`,
-  `game_moves` (the move journal), `complaints` and `account_stats`, and the
+  `game_moves` (the move journal), `complaints`, `account_stats` and
+  `account_best_move`, and the
   social/lobby tables `friendships` (the request/accept graph, its status admitting
   `declined`), `blocks`
   (per-user blocks), `chat_messages` (per-game chat and nudges, carrying the per-message
@@ -597,7 +598,17 @@ disguised robot stays indistinguishable from a person.
   seat): wins, losses, **draws**, max points in a game, and
   max points for a single **move** (which already folds in every word the move
   formed plus the all-tiles bonus). A tie increments draws only; a resignation or
-  timeout is a loss for the acting player.
+  timeout is a loss for the acting player. A companion table **`account_best_move`**
+  (keyed by account **and variant**) keeps the highest-scoring single play **per
+  variant** with the word itself: its main word as an ordered JSON array of tiles
+  (letter, tile value, blank flag — value 0 for a blank), so the statistics screen
+  renders it as game tiles without the variant's alphabet table. Blank flags are
+  taken from every blank ever placed in the game (equivalent to reading the final
+  board, since a placed tile never moves). It is replaced only by a strictly
+  higher-scoring play, written in the same finish transaction, and skipped for
+  guest/honest-AI games exactly like `account_stats`. It is filled forward only —
+  plays finished before the table existed are not back-populated (the aggregate
+  `max_word_points` still covers them numerically).
 
 ### 9.1 History invariant (must hold forever)
 

docs/FUNCTIONAL.md

@@ -230,6 +230,9 @@ game is throwaway). The client shares the `.gcg` file where the platform support
 it, otherwise downloads it. Statistics (durable accounts only):
 wins, losses, draws, max points in a game, and max points for a single move (the
 best play, which already includes every word it formed plus the all-tiles bonus).
+The best move is also broken down **per game variant**, showing the **word itself**
+drawn as game tiles (a wildcard shows its letter but no value) — one row per variant
+the player has played, omitting variants with no plays.
 A game that can no longer be continued — because a rule changed and an earlier
 move would now be illegal — is closed as a **draw** the moment someone opens it,
 never left stuck on an error: the move history shows an impersonal organizer note

docs/FUNCTIONAL_ru.md

@@ -234,6 +234,9 @@ UTC), суточного окна отсутствия (away; сетка по 10
 иначе скачивает его. Статистика (только у постоянных аккаунтов):
 победы, поражения, ничьи, макс. очков за партию и макс. очков за один ход (лучший
 ход, уже включающий все образованные им слова и бонус за все фишки).
+Лучший ход также даётся **с разбивкой по вариантам игры** — **само слово**,
+нарисованное игровыми фишками (wildcard показывает свою букву без очков), по одной
+строке на каждый сыгранный вариант; варианты без ходов не выводятся.
 Партия, которую больше нельзя продолжить — из-за изменения правил более ранний ход
 стал бы недопустимым, — закрывается **ничьёй** в момент открытия её игроком, а не
 остаётся висеть с ошибкой: в конце истории ходов показывается обезличенная заметка

docs/UI_DESIGN.md

@@ -280,8 +280,13 @@ enabled on the first, uncached load) and flip in place when an event refreshes t
   everywhere (score card, lobby row, turn line), the add-friend 🤝 is never drawn, and the chat's
   send field and 🛎️ nudge stay **disabled** while the 🔎 dictionary word-check keeps working.
 - **Statistics** (`screens/Stats.svelte`, the lobby 📊 tab): a 2-column grid of stat
-  cards (wins / losses / draws / games / win-rate / best game / best move) — pure
-  numbers, no charts.
+  cards (wins / losses / draws / games / win-rate / best game) — pure numbers, no
+  charts — followed by a **full-width "best move" card** that breaks the best move
+  down per variant: one row per played variant (catalogue order, empty variants
+  omitted) with the variant name on the left, the **word drawn as game tiles**
+  (`components/WordTiles.svelte`, the board's placed-tile look at a small fixed size;
+  a wildcard shows its letter but no value) right-aligned to a shared edge, and the
+  score right-aligned in its own column.
 - **Profile editing** (`screens/Profile.svelte`): an inline form — display name, a
   **UTC-offset** timezone dropdown (defaulting to the browser's offset), the away
   window as hour + 10-minute dropdowns (24-hour, ≤ 12 h), and block toggles — plus an