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/postgres/migrations/00001_baseline.sql

@@ -131,7 +131,8 @@ CREATE INDEX games_open_idx ON games (open_deadline_at) WHERE status = 'open';
 -- account, or NULL for the still-empty opponent seat of an auto-match game waiting for an
 -- opponent (status='open'); it is filled when a human or a robot joins. score is the
 -- running/final score, is_winner is stamped on finish (false for every seat on a draw),
--- hints_used counts the per-game allowance consumed before the profile wallet.
+-- hints_used counts the seat's total hints used this game (the free per-game allowance plus
+-- the wallet-charged ones; the first HintsPerPlayer are the allowance).
 CREATE TABLE game_players (
     game_id    uuid     NOT NULL REFERENCES games (game_id) ON DELETE CASCADE,
     seat       smallint NOT NULL,

backend/internal/postgres/migrations/00009_best_move.sql

@@ -0,0 +1,25 @@
+-- +goose Up
+-- Per-account, per-variant best single move: the highest-scoring play the account has
+-- ever made in each game variant. It exists so the statistics screen can show the word
+-- itself broken down by variant, not just the dimensionless aggregate
+-- account_stats.max_word_points. tiles is the move's main word as an ordered JSON array of
+-- {letter, value, blank} objects (value 0 and blank true for a wildcard), so the client
+-- renders it as game tiles without needing the variant's alphabet table. score is the
+-- play's total points (every word it formed plus the all-tiles bonus), matching
+-- max_word_points. A row is replaced only by a strictly higher-scoring play. It is written
+-- at game finish alongside account_stats; guest and honest-AI games never record statistics,
+-- so they never write here. See docs/ARCHITECTURE.md §9.
+SET search_path = backend, pg_catalog;
+
+CREATE TABLE account_best_move (
+    account_id uuid        NOT NULL REFERENCES accounts (account_id) ON DELETE CASCADE,
+    variant    text        NOT NULL,
+    score      integer     NOT NULL,
+    tiles      jsonb       NOT NULL,
+    updated_at timestamptz NOT NULL DEFAULT now(),
+    PRIMARY KEY (account_id, variant)
+);
+
+-- +goose Down
+SET search_path = backend, pg_catalog;
+DROP TABLE IF EXISTS account_best_move;

backend/internal/postgres/migrations/00010_stats_moves_hints.sql

@@ -0,0 +1,16 @@
+-- +goose Up
+-- account_stats gains two lifetime counters for the player's statistics screen: moves — the
+-- player's plays (tile placements; passes and exchanges do not count) — and hints_used — every
+-- hint the player took (the free per-game allowance plus the wallet-charged ones). Both are
+-- summed at game finish over the same games that feed the rest of account_stats (durable
+-- non-guest accounts; honest-AI games are skipped), so the screen can show the "hint share"
+-- = hints_used / moves. See docs/ARCHITECTURE.md §9.
+SET search_path = backend, pg_catalog;
+
+ALTER TABLE account_stats ADD COLUMN moves      integer NOT NULL DEFAULT 0;
+ALTER TABLE account_stats ADD COLUMN hints_used integer NOT NULL DEFAULT 0;
+
+-- +goose Down
+SET search_path = backend, pg_catalog;
+ALTER TABLE account_stats DROP COLUMN hints_used;
+ALTER TABLE account_stats DROP COLUMN moves;