Stage 17 round 6 (#4/#5/#6): draft persistence wire + gateway + UI

Complete the client-side draft feature on top of the shipped backend
foundation (the game_drafts store/service):

- FB: DraftRequest{game_id,json} + DraftView{json} (a draft get reuses
  GameActionRequest); regenerated committed Go + TS bindings.
- Backend REST: GET/PUT /games/:id/draft, a draftDTO
  (rack_order/board_tiles) mapped to game.Draft.
- Gateway: draft.get/draft.save transcode forwarding the composition
  JSON verbatim (json.RawMessage both ways -- no double-encode).
- UI: debounced save of the rack order + board tiles and restore on
  load (lib/draft.ts), plus #5 -- tiles may be arranged on the
  opponent's turn (placement relaxed; the preview and Make-move stay
  your-turn-only, so an off-turn draft is position-only).

Tests: backend handler validation, gateway pass-through round-trip, UI
draft/codec units, and a draft-restore e2e.

gateway/internal/backendclient/api.go

@@ -2,6 +2,7 @@ package backendclient
 
 import (
 	"context"
+	"encoding/json"
 	"net/http"
 	"net/url"
 	"strconv"
@@ -337,6 +338,21 @@ func (c *Client) Hint(ctx context.Context, userID, gameID string) (HintResultRes
 	return out, err
 }
 
+// GetDraft returns the player's saved composition for a game (Stage 17) as the backend's
+// raw JSON body. The gateway forwards it verbatim, never interpreting its shape.
+func (c *Client) GetDraft(ctx context.Context, userID, gameID string) (json.RawMessage, error) {
+	var out json.RawMessage
+	err := c.do(ctx, http.MethodGet, c.gamePath(gameID, "/draft"), userID, "", nil, &out)
+	return out, err
+}
+
+// SaveDraft upserts the player's composition for a game (Stage 17). body is the client's
+// {rack_order, board_tiles} JSON, forwarded verbatim — a json.RawMessage marshals as-is, so
+// there is no double-encode.
+func (c *Client) SaveDraft(ctx context.Context, userID, gameID string, body json.RawMessage) error {
+	return c.do(ctx, http.MethodPut, c.gamePath(gameID, "/draft"), userID, "", body, nil)
+}
+
 // Evaluate previews a tentative play's legality and score. The tiles are addressed by
 // alphabet index (Stage 13).
 func (c *Client) Evaluate(ctx context.Context, userID, gameID, dir string, tiles []PlayTileJSON) (EvalResultResp, error) {