feat(game): official first-move tile draw + admin step-by-step replay

Decide who moves first by the official rule: each seated player draws one
tile, the one closest to "A" leads (a blank beats every letter), ties
re-drawing until a single leader remains. Each draw uses honest per-draw
crypto/rand entropy (not the deterministic bag seed), so the recorded draw —
not a seed — is the only account of the outcome. The leader takes seat 0, so
the engine and journal replay are unchanged.

The draw is recorded with the game (game_setup_draws, migration 00013) for
future tournaments, designed as a discrete "player N draws a tile" step.
Friend/AI games draw at creation. Auto-match draws when the game opens,
against a synthetic uuid.Nil opponent whose draw rows (NULL account_id) are
back-filled to the real opponent on join — so the opener's seat is fixed up
front and the existing open-game pre-move is preserved with no reseating.

Admin /_gm/games/:id gains the recorded draw list and a simple step-by-step
board replay (game.ReplayTimeline + a vanilla-JS stepper): a board with
A-O/1-15 headers and highlighted premium squares, placed letters with their
tile value as a subscript, rack panels around the board (seat 0 top, 1
bottom, 2 left, 3 right) with the current player highlighted, and a per-move
log with the tiles drawn and the bag remainder.

Docs: ARCHITECTURE §6/§9, FUNCTIONAL (+_ru), PRERELEASE (FM row), design spec.

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

@@ -0,0 +1,24 @@
+//
+// 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 GameSetupDraws struct {
+	GameID    uuid.UUID `sql:"primary_key"`
+	Round     int16     `sql:"primary_key"`
+	PickNo    int16     `sql:"primary_key"`
+	AccountID *uuid.UUID
+	Letter    string
+	IsBlank   bool
+	DrawRank  int16
+	CreatedAt time.Time
+}

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

@@ -0,0 +1,99 @@
+//
+// 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 GameSetupDraws = newGameSetupDrawsTable("backend", "game_setup_draws", "")
+
+type gameSetupDrawsTable struct {
+	postgres.Table
+
+	// Columns
+	GameID    postgres.ColumnString
+	Round     postgres.ColumnInteger
+	PickNo    postgres.ColumnInteger
+	AccountID postgres.ColumnString
+	Letter    postgres.ColumnString
+	IsBlank   postgres.ColumnBool
+	DrawRank  postgres.ColumnInteger
+	CreatedAt postgres.ColumnTimestampz
+
+	AllColumns     postgres.ColumnList
+	MutableColumns postgres.ColumnList
+	DefaultColumns postgres.ColumnList
+}
+
+type GameSetupDrawsTable struct {
+	gameSetupDrawsTable
+
+	EXCLUDED gameSetupDrawsTable
+}
+
+// AS creates new GameSetupDrawsTable with assigned alias
+func (a GameSetupDrawsTable) AS(alias string) *GameSetupDrawsTable {
+	return newGameSetupDrawsTable(a.SchemaName(), a.TableName(), alias)
+}
+
+// Schema creates new GameSetupDrawsTable with assigned schema name
+func (a GameSetupDrawsTable) FromSchema(schemaName string) *GameSetupDrawsTable {
+	return newGameSetupDrawsTable(schemaName, a.TableName(), a.Alias())
+}
+
+// WithPrefix creates new GameSetupDrawsTable with assigned table prefix
+func (a GameSetupDrawsTable) WithPrefix(prefix string) *GameSetupDrawsTable {
+	return newGameSetupDrawsTable(a.SchemaName(), prefix+a.TableName(), a.TableName())
+}
+
+// WithSuffix creates new GameSetupDrawsTable with assigned table suffix
+func (a GameSetupDrawsTable) WithSuffix(suffix string) *GameSetupDrawsTable {
+	return newGameSetupDrawsTable(a.SchemaName(), a.TableName()+suffix, a.TableName())
+}
+
+func newGameSetupDrawsTable(schemaName, tableName, alias string) *GameSetupDrawsTable {
+	return &GameSetupDrawsTable{
+		gameSetupDrawsTable: newGameSetupDrawsTableImpl(schemaName, tableName, alias),
+		EXCLUDED:            newGameSetupDrawsTableImpl("", "excluded", ""),
+	}
+}
+
+func newGameSetupDrawsTableImpl(schemaName, tableName, alias string) gameSetupDrawsTable {
+	var (
+		GameIDColumn    = postgres.StringColumn("game_id")
+		RoundColumn     = postgres.IntegerColumn("round")
+		PickNoColumn    = postgres.IntegerColumn("pick_no")
+		AccountIDColumn = postgres.StringColumn("account_id")
+		LetterColumn    = postgres.StringColumn("letter")
+		IsBlankColumn   = postgres.BoolColumn("is_blank")
+		DrawRankColumn  = postgres.IntegerColumn("draw_rank")
+		CreatedAtColumn = postgres.TimestampzColumn("created_at")
+		allColumns      = postgres.ColumnList{GameIDColumn, RoundColumn, PickNoColumn, AccountIDColumn, LetterColumn, IsBlankColumn, DrawRankColumn, CreatedAtColumn}
+		mutableColumns  = postgres.ColumnList{AccountIDColumn, LetterColumn, IsBlankColumn, DrawRankColumn, CreatedAtColumn}
+		defaultColumns  = postgres.ColumnList{IsBlankColumn, CreatedAtColumn}
+	)
+
+	return gameSetupDrawsTable{
+		Table: postgres.NewTable(schemaName, tableName, alias, allColumns...),
+
+		//Columns
+		GameID:    GameIDColumn,
+		Round:     RoundColumn,
+		PickNo:    PickNoColumn,
+		AccountID: AccountIDColumn,
+		Letter:    LetterColumn,
+		IsBlank:   IsBlankColumn,
+		DrawRank:  DrawRankColumn,
+		CreatedAt: CreatedAtColumn,
+
+		AllColumns:     allColumns,
+		MutableColumns: mutableColumns,
+		DefaultColumns: defaultColumns,
+	}
+}

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

@@ -31,6 +31,7 @@ func UseSchema(schema string) {
 	GameInvitations = GameInvitations.FromSchema(schema)
 	GameMoves = GameMoves.FromSchema(schema)
 	GamePlayers = GamePlayers.FromSchema(schema)
+	GameSetupDraws = GameSetupDraws.FromSchema(schema)
 	Games = Games.FromSchema(schema)
 	Identities = Identities.FromSchema(schema)
 	Sessions = Sessions.FromSchema(schema)