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/engine/setup.go

@@ -0,0 +1,52 @@
+package engine
+
+import "fmt"
+
+// SetupTile is one tile of a variant's full bag, decoded for the first-move draw
+// (docs/ARCHITECTURE.md §6): its concrete letter (or the blank marker), a blank
+// flag, and its draw rank. Lower rank wins the draw — a blank ranks above every
+// letter, and letters rank by alphabet index, so the tile closest to the start of
+// the alphabet ("A") wins. It is dictionary-independent, built from the variant's
+// solver ruleset alone.
+type SetupTile struct {
+	// Letter is the concrete character (the case the solver ruleset emits), or
+	// the blank marker "?" for a blank.
+	Letter string
+	// Blank reports whether the tile is a blank.
+	Blank bool
+	// Rank orders the draw: BlankRank for a blank (best), else the letter's
+	// alphabet index (0 = closest to "A").
+	Rank int
+}
+
+// BlankRank is the first-move draw rank of a blank: below every letter index, so a
+// blank always beats a lettered tile, matching the official rule that a blank
+// supersedes all letters.
+const BlankRank = -1
+
+// SetupBag returns variant's full tile bag — every lettered tile expanded by its
+// count, plus one entry per blank — decoded for the first-move seeding draw. The
+// order is deterministic (alphabet order, blanks last); callers shuffle it with
+// their own entropy. It needs no dictionary, so it is built from the variant's
+// ruleset alone and reports ErrUnknownVariant for an unrecognised variant.
+func SetupBag(v Variant) ([]SetupTile, error) {
+	rs, ok := v.ruleset()
+	if !ok {
+		return nil, fmt.Errorf("%w: %d", ErrUnknownVariant, v)
+	}
+	bag := make([]SetupTile, 0, 128)
+	for i, n := range rs.Counts {
+		ch, err := rs.Alphabet.Character(byte(i))
+		if err != nil {
+			// An offered variant's alphabet never yields a bad index; skip defensively.
+			continue
+		}
+		for range n {
+			bag = append(bag, SetupTile{Letter: ch, Rank: i})
+		}
+	}
+	for range rs.Blanks {
+		bag = append(bag, SetupTile{Letter: blankLetter, Blank: true, Rank: BlankRank})
+	}
+	return bag, nil
+}

backend/internal/engine/setup_test.go

@@ -0,0 +1,47 @@
+package engine
+
+import (
+	"errors"
+	"testing"
+)
+
+func TestSetupBagEnglish(t *testing.T) {
+	bag, err := SetupBag(VariantEnglish)
+	if err != nil {
+		t.Fatalf("SetupBag: %v", err)
+	}
+	// English Scrabble: 98 lettered tiles + 2 blanks = 100.
+	if len(bag) != 100 {
+		t.Fatalf("bag size = %d, want 100", len(bag))
+	}
+	blanks, aCount := 0, 0
+	for _, tl := range bag {
+		switch {
+		case tl.Blank:
+			blanks++
+			if tl.Rank != BlankRank {
+				t.Errorf("blank rank = %d, want %d", tl.Rank, BlankRank)
+			}
+			if tl.Letter != blankLetter {
+				t.Errorf("blank letter = %q, want %q", tl.Letter, blankLetter)
+			}
+		case tl.Letter == "a":
+			aCount++
+			if tl.Rank != 0 {
+				t.Errorf("'a' rank = %d, want 0 (closest to A)", tl.Rank)
+			}
+		}
+	}
+	if blanks != 2 {
+		t.Errorf("blanks = %d, want 2", blanks)
+	}
+	if aCount != 9 {
+		t.Errorf("'a' count = %d, want 9", aCount)
+	}
+}
+
+func TestSetupBagUnknownVariant(t *testing.T) {
+	if _, err := SetupBag(Variant(99)); !errors.Is(err, ErrUnknownVariant) {
+		t.Fatalf("err = %v, want ErrUnknownVariant", err)
+	}
+}