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/jet/backend/model/account_best_move.go

@@ -0,0 +1,21 @@
+//
+// Code generated by go-jet DO NOT EDIT.
+//
+// WARNING: Changes to this file may cause incorrect behavior
+// and will be lost if the code is regenerated
+//
+
+package model
+
+import (
+	"github.com/google/uuid"
+	"time"
+)
+
+type AccountBestMove struct {
+	AccountID uuid.UUID `sql:"primary_key"`
+	Variant   string    `sql:"primary_key"`
+	Score     int32
+	Tiles     string
+	UpdatedAt time.Time
+}

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_best_move.go

@@ -0,0 +1,90 @@
+//
+// Code generated by go-jet DO NOT EDIT.
+//
+// WARNING: Changes to this file may cause incorrect behavior
+// and will be lost if the code is regenerated
+//
+
+package table
+
+import (
+	"github.com/go-jet/jet/v2/postgres"
+)
+
+var AccountBestMove = newAccountBestMoveTable("backend", "account_best_move", "")
+
+type accountBestMoveTable struct {
+	postgres.Table
+
+	// Columns
+	AccountID postgres.ColumnString
+	Variant   postgres.ColumnString
+	Score     postgres.ColumnInteger
+	Tiles     postgres.ColumnString
+	UpdatedAt postgres.ColumnTimestampz
+
+	AllColumns     postgres.ColumnList
+	MutableColumns postgres.ColumnList
+	DefaultColumns postgres.ColumnList
+}
+
+type AccountBestMoveTable struct {
+	accountBestMoveTable
+
+	EXCLUDED accountBestMoveTable
+}
+
+// AS creates new AccountBestMoveTable with assigned alias
+func (a AccountBestMoveTable) AS(alias string) *AccountBestMoveTable {
+	return newAccountBestMoveTable(a.SchemaName(), a.TableName(), alias)
+}
+
+// Schema creates new AccountBestMoveTable with assigned schema name
+func (a AccountBestMoveTable) FromSchema(schemaName string) *AccountBestMoveTable {
+	return newAccountBestMoveTable(schemaName, a.TableName(), a.Alias())
+}
+
+// WithPrefix creates new AccountBestMoveTable with assigned table prefix
+func (a AccountBestMoveTable) WithPrefix(prefix string) *AccountBestMoveTable {
+	return newAccountBestMoveTable(a.SchemaName(), prefix+a.TableName(), a.TableName())
+}
+
+// WithSuffix creates new AccountBestMoveTable with assigned table suffix
+func (a AccountBestMoveTable) WithSuffix(suffix string) *AccountBestMoveTable {
+	return newAccountBestMoveTable(a.SchemaName(), a.TableName()+suffix, a.TableName())
+}
+
+func newAccountBestMoveTable(schemaName, tableName, alias string) *AccountBestMoveTable {
+	return &AccountBestMoveTable{
+		accountBestMoveTable: newAccountBestMoveTableImpl(schemaName, tableName, alias),
+		EXCLUDED:             newAccountBestMoveTableImpl("", "excluded", ""),
+	}
+}
+
+func newAccountBestMoveTableImpl(schemaName, tableName, alias string) accountBestMoveTable {
+	var (
+		AccountIDColumn = postgres.StringColumn("account_id")
+		VariantColumn   = postgres.StringColumn("variant")
+		ScoreColumn     = postgres.IntegerColumn("score")
+		TilesColumn     = postgres.StringColumn("tiles")
+		UpdatedAtColumn = postgres.TimestampzColumn("updated_at")
+		allColumns      = postgres.ColumnList{AccountIDColumn, VariantColumn, ScoreColumn, TilesColumn, UpdatedAtColumn}
+		mutableColumns  = postgres.ColumnList{ScoreColumn, TilesColumn, UpdatedAtColumn}
+		defaultColumns  = postgres.ColumnList{UpdatedAtColumn}
+	)
+
+	return accountBestMoveTable{
+		Table: postgres.NewTable(schemaName, tableName, alias, allColumns...),
+
+		//Columns
+		AccountID: AccountIDColumn,
+		Variant:   VariantColumn,
+		Score:     ScoreColumn,
+		Tiles:     TilesColumn,
+		UpdatedAt: UpdatedAtColumn,
+
+		AllColumns:     allColumns,
+		MutableColumns: mutableColumns,
+		DefaultColumns: defaultColumns,
+	}
+}

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,