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/game/replay_timeline.go

@@ -0,0 +1,144 @@
+package game
+
+import (
+	"context"
+	"errors"
+	"fmt"
+
+	"github.com/google/uuid"
+
+	"scrabble/backend/internal/engine"
+)
+
+// ReplayStep is one step of an admin game replay: the move that produced it (nil for the
+// initial dealt state, step 0) and the resulting position — every seat's rack, the running
+// scores, whose turn it is and the bag remainder. Step k's board is the union of every
+// play's placements through step k, which the renderer accumulates onto an empty grid
+// (docs/ARCHITECTURE.md §9.1 visual replay).
+type ReplayStep struct {
+	// Move is the journalled move that produced this state, or nil for the initial deal.
+	Move *HistoryMove
+	// Drawn lists the tiles the mover drew from the bag after this move ("?" for a blank);
+	// empty for the initial deal, a pass or a resignation.
+	Drawn []string
+	// Racks holds every seat's rack at this step, indexed by seat ("?" for a blank).
+	Racks [][]string
+	// Scores holds every seat's running score, indexed by seat.
+	Scores []int
+	// ToMove is the seat to move at this step.
+	ToMove int
+	// BagLen is the number of tiles left in the bag at this step.
+	BagLen int
+}
+
+// ReplayTimelineView is the admin replay of a game: the persisted game plus the ordered
+// replay steps (the initial deal followed by one step per journalled move).
+type ReplayTimelineView struct {
+	Game  Game
+	Steps []ReplayStep
+}
+
+// ReplayTimeline rebuilds a game from its pinned seed and journal and returns the ordered
+// replay steps for the admin console: the initial deal (step 0) then one step per
+// journalled move, each carrying the resulting racks, scores, turn cursor, bag size and the
+// tiles the mover drew. The deterministic bag makes the reconstruction exact. It needs no
+// dictionary beyond the engine the seed deals, and — like the live replay — stops early if a
+// committed move became illegal under tightened rules rather than failing.
+func (svc *Service) ReplayTimeline(ctx context.Context, gameID uuid.UUID) (ReplayTimelineView, error) {
+	pre, err := svc.store.GetGame(ctx, gameID)
+	if err != nil {
+		return ReplayTimelineView{}, err
+	}
+	seed, err := svc.store.GameSeed(ctx, gameID)
+	if err != nil {
+		return ReplayTimelineView{}, err
+	}
+	g, err := engine.New(svc.registry, engine.Options{
+		Variant:              pre.Variant,
+		Version:              pre.DictVersion,
+		Players:              pre.Players,
+		Seed:                 seed,
+		DropoutTiles:         pre.DropoutTiles,
+		MultipleWordsPerTurn: pre.MultipleWordsPerTurn,
+	})
+	if err != nil {
+		return ReplayTimelineView{}, err
+	}
+	moves, err := svc.store.GetJournal(ctx, gameID)
+	if err != nil {
+		return ReplayTimelineView{}, err
+	}
+	steps := make([]ReplayStep, 0, len(moves)+1)
+	steps = append(steps, snapshotStep(g, nil, nil))
+	for i := range moves {
+		mv := moves[i]
+		before := g.Hand(mv.Seat)
+		if err := replayMove(g, mv); err != nil {
+			if errors.Is(err, engine.ErrIllegalPlay) {
+				g.Abort()
+				break
+			}
+			return ReplayTimelineView{}, fmt.Errorf("game: replay-timeline %s move %d: %w", gameID, mv.Seq, err)
+		}
+		moveCopy := mv
+		steps = append(steps, snapshotStep(g, &moveCopy, drawnTiles(before, g.Hand(mv.Seat), usedTiles(mv))))
+	}
+	return ReplayTimelineView{Game: pre, Steps: steps}, nil
+}
+
+// snapshotStep captures the position after applying move (nil for the initial deal): every
+// seat's rack and score, the turn cursor and the bag size, with the supplied drawn tiles.
+func snapshotStep(g *engine.Game, move *HistoryMove, drawn []string) ReplayStep {
+	n := g.Players()
+	racks := make([][]string, n)
+	scores := make([]int, n)
+	for i := 0; i < n; i++ {
+		racks[i] = g.Hand(i)
+		scores[i] = g.Score(i)
+	}
+	return ReplayStep{Move: move, Drawn: drawn, Racks: racks, Scores: scores, ToMove: g.ToMove(), BagLen: g.BagLen()}
+}
+
+// usedTiles returns the rack tiles a move consumed ("?" for a blank): the placed tiles of a
+// play or the swapped tiles of an exchange; a pass or resignation consumes none.
+func usedTiles(mv HistoryMove) []string {
+	switch mv.Action {
+	case "play":
+		used := make([]string, len(mv.Tiles))
+		for i, t := range mv.Tiles {
+			if t.Blank {
+				used[i] = "?" // a placed blank leaves the rack as the blank marker
+			} else {
+				used[i] = t.Letter
+			}
+		}
+		return used
+	case "exchange":
+		return mv.Exchanged
+	}
+	return nil
+}
+
+// drawnTiles returns the tiles the mover drew from the bag: the post-move rack (after) minus
+// the tiles kept (before minus used). It compares the racks as multisets, so duplicate
+// letters are counted correctly.
+func drawnTiles(before, after, used []string) []string {
+	kept := make(map[string]int, len(before))
+	for _, t := range before {
+		kept[t]++
+	}
+	for _, t := range used {
+		if kept[t] > 0 {
+			kept[t]--
+		}
+	}
+	var drawn []string
+	for _, t := range after {
+		if kept[t] > 0 {
+			kept[t]--
+			continue
+		}
+		drawn = append(drawn, t)
+	}
+	return drawn
+}