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.

docs/superpowers/specs/2026-06-19-first-move-draw-design.md

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+# First-move tile-draw seeding + admin game replay — design
+
+- Date: 2026-06-19
+- Branch: `feature/first-move-draw`
+- Status: approved (owner sign-off 2026-06-19)
+
+## Goal
+
+Two linked pieces.
+
+1. **First-move selection by the official rule.** Each seated player draws one tile
+   from the bag; the tile alphabetically closest to "A" wins, a blank superseding all
+   letters. Players tied for the best tile re-draw until a single leader remains. Each
+   draw uses fresh entropy — **not** the game's deterministic seed. The whole draw
+   process is persisted with the game (not shown to players yet; needed later for
+   tournaments, where the draw becomes a manual, per-tile external "player N draws a
+   tile" call). A game must not start until the draw has produced a leader. The future
+   API is not designed here, but the code exposes the draw as a discrete step.
+
+2. **Admin replay on `/_gm/games/:id`.** A simple board that steps move-by-move:
+   column (A–O) and row (1–15) headers, highlighted premium squares, placed letters
+   drawn upper-case with the tile value as a subscript (0 → no number), rack panels
+   around the board (seat 0 top, 1 bottom, 2 left, 3 right) labelled by player name
+   with a profile link and the current player's rack highlighted, prev/next stepping,
+   and a per-move log line with the move, the tiles drawn from the bag, and the bag
+   remainder. The first-move draw is shown as a flat list of actions, not stepped on
+   the board.
+
+## Decisions (owner interview, 2026-06-19)
+
+- **Comparison key:** alphabetical (alphabet index; closest to "A" wins; blank
+  supersedes). Not tile point value.
+- **The draw decides only the first player;** the rest keep their seating order (the
+  circle is rotated so the winner leads).
+- **Persistence:** a dedicated table `game_setup_draws` (one row per draw),
+  tournament / manual-API ready.
+- **Lifecycle:** a code seam only (a seeding component with a per-draw method); no
+  persisted `seeding` status yet (the auto path runs it synchronously at the active
+  transition).
+
+## Design
+
+### Seeding (`internal/game/seating.go`)
+
+- A component shaped as a finite state machine, ready for a future per-tile external
+  call. Entropy is a parameter (interface / `io.Reader`); production uses
+  `crypto/rand`, tests inject a deterministic source so the ranking / tie / rotation
+  logic is unit-testable.
+- **A round:** honestly shuffle the variant's full tile multiset (`rules.Counts` +
+  blanks) with fresh entropy and draw one tile **without replacement** for each
+  participant. This realises "shuffle before each draw, not a single seed".
+- **Rank:** blank = best (`-1`); letter = alphabet index (`0` = closest to "A").
+  Lower rank moves earlier.
+- **Tie:** participants sharing the best rank re-draw in the next round (others drop
+  out) until a single leader remains.
+- **Result:** the winner plus the full draw log.
+
+### Turn order — seat rotation
+
+The draw affects the game only through who occupies **seat 0** (seat 0 moves first;
+the engine/replay invariant is unchanged). Rotate the seated-account circle so the
+winner sits at seat 0, preserving the cyclic order of the rest. This generalises the
+current `seed&1` swap (2 players) and replaces both `seed&1` (auto-match) and
+"`Seats[0]` first" (friend/AI). It applies to every new game.
+
+The engine deals racks by seat **index** and is account-agnostic, and journal replay
+starts at seat 0, so **no engine or replay change is needed** — only the seat→account
+mapping in `game_players`.
+
+### Persistence — `game_setup_draws` (migration `00013`)
+
+```sql
+CREATE TABLE backend.game_setup_draws (
+    game_id    uuid        NOT NULL REFERENCES backend.games (game_id) ON DELETE CASCADE,
+    round      smallint    NOT NULL,
+    pick_no    smallint    NOT NULL,
+    account_id uuid        NOT NULL REFERENCES backend.accounts (account_id),
+    letter     text        NOT NULL,
+    is_blank   boolean     NOT NULL DEFAULT false,
+    rank       smallint    NOT NULL,
+    created_at timestamptz NOT NULL DEFAULT now(),
+    PRIMARY KEY (game_id, round, pick_no)
+);
+```
+
+Self-contained and dictionary-independent (decoded letter + blank flag + numeric
+rank), like the §9.1 journal. The first mover is visible as seat 0 in `game_players`,
+so there is no redundant column. Additive — existing games have no rows (no backfill).
+The future tournament API appends one row per draw call.
+
+### Wiring — the active transition
+
+- **Create (friend/AI):** run the seeding over `params.Seats`, persist the draw rows,
+  rotate the account list so the winner is index 0, then proceed unchanged
+  (`engine.New` takes only the seat count). All within the create transaction.
+- **Auto-match:** the second player is unknown until the seat is filled, so the
+  seeding runs at `fillOpenSeat` (human join) and `AttachRobot` (robot) inside the
+  fill transaction. The seat assignment is written from the draw outcome (seat 0 =
+  winner) rather than only filling the empty seat; the open-time `seed&1` pre-seating
+  is dropped.
+
+The auto path calls the seeding component synchronously in a loop. No persisted
+`seeding` status; the seam in code is what a future manual API drives.
+
+### Admin replay
+
+- **Data:** a new service method `ReplayTimeline(gameID)` reuses the existing
+  `replay()` (engine rebuilt from seed + journal) and snapshots after each move: every
+  seat's rack (`Hand(i)`), score (`Score(i)`), the seat to move (`ToMove()`), the bag
+  remainder (`BagLen()`), plus per move the action, placements, words, and the tiles
+  drawn from the bag (multiset diff: `hand_after − (hand_before − used)`; `hand_before`
+  from the journal). Step 0 is the dealt racks. The board at step k is the placements
+  of plays 1..k applied onto an empty grid (no dictionary — §9.1 visual replay).
+- **UI:** server-rendered Go `html/template` plus a small page-scoped vanilla-JS
+  stepper over the timeline embedded as JSON (no per-step round-trip). The board
+  renders headers, highlighted premium squares (a standard fixed 15×15 layout
+  duplicated as a Go constant — `premiums.ts` is itself such a constant; the admin is
+  not coupled to solver internals), upper-case letters with the value subscript (0 → no
+  number) in tile-styled cells. Rack panels: seat 0 top, 1 bottom, 2 left, 3 right;
+  name + profile link; the current player's rack highlighted. A log accumulates by move
+  (play / pass / exchange + drawn tiles + bag remainder), the current step highlighted.
+  The seeding is a separate flat list ("Round N: player X — E(rank), … → Y leads
+  first"), with profile links.
+
+## Tests
+
+- **Seeding:** ranking (blank beats letters; closer to "A" wins), tie chains, rotation
+  for 2/3/4 seats, record determinism under an injected entropy source.
+- **ReplayTimeline:** drawn tiles / bag remainder / racks / scores on a known short
+  game.
+- **Store / integration:** write+read `game_setup_draws`; seat 0 = winner for both
+  Create and auto-match.
+
+## Out of scope
+
+The tournament draw API itself (only the seam). No change to the game bag's
+determinism or replay. No reuse / rewrite of the Svelte board in the admin. The board
+design is deliberately minimal.
+
+## Docs to bake back (same PR)
+
+`docs/ARCHITECTURE.md` (§6 seeding procedure, §9 table, §9.1-style record invariant),
+`docs/FUNCTIONAL.md` (+ `_ru`) first-move-selection story, backend / admin READMEs, Go
+Doc comments, `PRERELEASE.md` note.
+
+## Update (2026-06-20) — final auto-match design
+
+During implementation the owner replaced the auto-match approach. The original plan above ran
+the draw at **fill** time (when the opponent joins) and **reseated** the winner to seat 0. That
+conflicts with the existing open-game feature where the opener may play their opening move
+while waiting: reseating after a move would corrupt the journal's seat↔move mapping.
+
+The final design runs the draw when the game **opens**, with the not-yet-arrived opponent as a
+synthetic placeholder (`uuid.Nil`). The draw fixes the opener's seat up front; the opponent
+joins into the already-decided empty seat with **no reseating**, so the open-game pre-move is
+preserved and the journal is never disturbed. The opponent's draw rows are persisted with a
+NULL `account_id` (so `game_setup_draws.account_id` is **nullable**) and **back-filled** to the
+real opponent (or robot) on join. The directly-seated (friend/AI) path is unchanged from the
+plan (draw at create, real accounts, no synthetic). Consequently there is **no play-gating and
+no rack-hiding** while a game is open. See `docs/ARCHITECTURE.md` §6 / §9 for the authoritative
+description.