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.

docs/ARCHITECTURE.md

@@ -203,7 +203,8 @@ arrive from a platform rather than completing a mandatory registration).
   guest is promoted to durable, clearing `is_guest`).
 - **Merge** retires the account that owns the linked identity into the **current**
   account, in a single transaction (`internal/accountmerge`): statistics summed
-  (max points kept), the hint wallet summed, `paid_account` ORed, identities
+  (counters incl. moves/hints added, max points kept, and the per-variant best moves
+  merged keeping the higher-scoring play), the hint wallet summed, `paid_account` ORed, identities
   repointed, games / chat / complaints transferred, friends and blocks
   de-duplicated (friendships keep the strongest status accepted>pending>declined),
   pending invitations/codes dropped, and the secondary kept as an **audit
@@ -347,7 +348,13 @@ Key points:
   placement and leaves the commit to the player. When the rack has no legal move the
   service spends **nothing** and returns `ErrNoHintAvailable` — surfaced as the distinct
   result code `no_hint_available` (separate from `hint_unavailable`) so the UI can say
-  "no options" rather than "no hints left".
+  "no options" rather than "no hints left". The hint count shown to the player is the
+  per-game allowance remaining **plus** the global wallet; because the wallet is global,
+  `game.state`/`game.hint` carry it as a separate `wallet_balance` field beside the combined
+  `hints_remaining`, so the client derives the per-game allowance (`hints_remaining -
+  wallet_balance`, which it may cache per game) and reads the wallet **live** from the
+  profile — otherwise a wallet hint spent in one game would leave a stale, too-high count
+  cached on every other game.
 - **Word-check tool**: unlimited dictionary lookups against the game's pinned
   dictionary; each result offers a **complaint** (complainant, game, variant,
   dict_version, word, the disputed result, an optional note) that lands in the admin
@@ -568,7 +575,8 @@ 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
@@ -596,8 +604,21 @@ disguised robot stays indistinguishable from a person.
   non-guest accounts only — the finish-time recompute skips any `is_guest`
   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.
+  formed plus the all-tiles bonus); plus two summed counters — `moves` (the player's
+  plays, i.e. tile placements; passes and exchanges do not count) and `hints_used`
+  (every hint taken, allowance + wallet) — from which the screen derives the **hint
+  share** = hints_used / moves. A tie increments draws only; a resignation or
+  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)