feat(stats): per-game hints used + lifetime moves and hint share

Store the hints a player used in each game, and add two lifetime tiles —
Moves and Hint share — to the statistics screen.

- per-game: game_players.hints_used now counts EVERY hint (allowance + wallet),
  not just the free allowance, so it is the seat's true total hints used this
  game. The allowance decision (used < HintsPerPlayer) and the hint badge values
  (hints_remaining / wallet_balance) are unchanged — the lobby hint-count fix does
  NOT regress; only the admin "hints used" column, which silently under-counted
  wallet hints, becomes accurate.
- account_stats gains two summed counters: moves (the player's plays — passes and
  exchanges excluded) and hints_used (every hint). Computed at game finish in
  buildStats over the same non-guest, non-honest-AI games as the rest of the stats.
- wire: StatsView gains moves + hints_used (trailing); gateway + UI codec + model;
  regen.
- ui: two tiles (Moves, Hint share = hints_used/moves, one-decimal % in the active
  locale); card order games·wins·draws·losses·moves·hint-share·best game·win-rate.
- docs: ARCHITECTURE §9 + baseline comment, FUNCTIONAL (+ru), UI_DESIGN.

Tests: TestHintPolicy (hints_used counts the wallet hint), TestGameLifecycleAndStats
(moves>0, hints=0), gateway stats round-trip, UI hintShare unit + codec + e2e.

backend/internal/postgres/jet/backend/model/account_stats.go

@@ -20,4 +20,6 @@ type AccountStats struct {
 	MaxGamePoints int32
 	MaxWordPoints int32
 	UpdatedAt     time.Time
+	Moves         int32
+	HintsUsed     int32
 }

backend/internal/postgres/jet/backend/table/account_stats.go

@@ -24,6 +24,8 @@ type accountStatsTable struct {
 	MaxGamePoints postgres.ColumnInteger
 	MaxWordPoints postgres.ColumnInteger
 	UpdatedAt     postgres.ColumnTimestampz
+	Moves         postgres.ColumnInteger
+	HintsUsed     postgres.ColumnInteger
 
 	AllColumns     postgres.ColumnList
 	MutableColumns postgres.ColumnList
@@ -72,9 +74,11 @@ func newAccountStatsTableImpl(schemaName, tableName, alias string) accountStatsT
 		MaxGamePointsColumn = postgres.IntegerColumn("max_game_points")
 		MaxWordPointsColumn = postgres.IntegerColumn("max_word_points")
 		UpdatedAtColumn     = postgres.TimestampzColumn("updated_at")
-		allColumns          = postgres.ColumnList{AccountIDColumn, WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn}
-		mutableColumns      = postgres.ColumnList{WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn}
-		defaultColumns      = postgres.ColumnList{WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn}
+		MovesColumn         = postgres.IntegerColumn("moves")
+		HintsUsedColumn     = postgres.IntegerColumn("hints_used")
+		allColumns          = postgres.ColumnList{AccountIDColumn, WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn, MovesColumn, HintsUsedColumn}
+		mutableColumns      = postgres.ColumnList{WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn, MovesColumn, HintsUsedColumn}
+		defaultColumns      = postgres.ColumnList{WinsColumn, LossesColumn, DrawsColumn, MaxGamePointsColumn, MaxWordPointsColumn, UpdatedAtColumn, MovesColumn, HintsUsedColumn}
 	)
 
 	return accountStatsTable{
@@ -88,6 +92,8 @@ func newAccountStatsTableImpl(schemaName, tableName, alias string) accountStatsT
 		MaxGamePoints: MaxGamePointsColumn,
 		MaxWordPoints: MaxWordPointsColumn,
 		UpdatedAt:     UpdatedAtColumn,
+		Moves:         MovesColumn,
+		HintsUsed:     HintsUsedColumn,
 
 		AllColumns:     allColumns,
 		MutableColumns: mutableColumns,

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/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;