feat(ui): single-word rule indicators + auto-match select redesign

Surface the per-game "single word" rule to the client and refine the
random-opponent New Game screen.

- Wire: thread multiple_words_per_turn into the GameView and Invitation
  FlatBuffers tables (Go + TS regenerated), through pkg/wire builders and both
  the backend push-event and gateway REST paths.
- In-game indicators (single-word games only): a small 1 in the status bar's
  score-preview slot (yields to the live preview) and a centred "One word per
  turn" label in the history-drawer header. Standard games show neither.
- Invitation card gains a "One word per turn" line for single-word invitations.
- Auto-match redesign: variant plaques are mutually-exclusive selects (highlight
  on tap, no longer enqueue); a lone offered variant is pre-selected; a bottom
  "Start game" button (disabled until a variant is chosen) confirms. The rule
  toggle appears once a Russian variant is selected.
- Tests: e2e for the new auto flow and the in-game indicator (mock g3 is a
  single-word game); mock/data + fixtures carry the new field. Docs: UI_DESIGN.

backend/internal/notify/encode.go

@@ -28,17 +28,18 @@ func toWireGame(g GameSummary) wire.GameView {
 		}
 	}
 	return wire.GameView{
-		ID:               g.ID,
-		Variant:          g.Variant,
-		DictVersion:      g.DictVersion,
-		Status:           g.Status,
-		Players:          g.Players,
-		ToMove:           g.ToMove,
-		TurnTimeoutSecs:  g.TurnTimeoutSecs,
-		MoveCount:        g.MoveCount,
-		EndReason:        g.EndReason,
-		Seats:            seats,
-		LastActivityUnix: g.LastActivityUnix,
+		ID:                   g.ID,
+		Variant:              g.Variant,
+		DictVersion:          g.DictVersion,
+		Status:               g.Status,
+		Players:              g.Players,
+		ToMove:               g.ToMove,
+		TurnTimeoutSecs:      g.TurnTimeoutSecs,
+		MultipleWordsPerTurn: g.MultipleWordsPerTurn,
+		MoveCount:            g.MoveCount,
+		EndReason:            g.EndReason,
+		Seats:                seats,
+		LastActivityUnix:     g.LastActivityUnix,
 	}
 }
 
@@ -102,16 +103,17 @@ func buildInvitation(b *flatbuffers.Builder, inv InvitationSummary) flatbuffers.
 		}
 	}
 	return wire.BuildInvitation(b, wire.Invitation{
-		ID:              inv.ID,
-		Inviter:         wire.AccountRef{AccountID: inv.Inviter.AccountID, DisplayName: inv.Inviter.DisplayName},
-		Invitees:        invitees,
-		Variant:         inv.Variant,
-		TurnTimeoutSecs: inv.TurnTimeoutSecs,
-		HintsAllowed:    inv.HintsAllowed,
-		HintsPerPlayer:  inv.HintsPerPlayer,
-		DropoutTiles:    inv.DropoutTiles,
-		Status:          inv.Status,
-		GameID:          inv.GameID,
-		ExpiresAtUnix:   inv.ExpiresAtUnix,
+		ID:                   inv.ID,
+		Inviter:              wire.AccountRef{AccountID: inv.Inviter.AccountID, DisplayName: inv.Inviter.DisplayName},
+		Invitees:             invitees,
+		Variant:              inv.Variant,
+		TurnTimeoutSecs:      inv.TurnTimeoutSecs,
+		HintsAllowed:         inv.HintsAllowed,
+		HintsPerPlayer:       inv.HintsPerPlayer,
+		MultipleWordsPerTurn: inv.MultipleWordsPerTurn,
+		DropoutTiles:         inv.DropoutTiles,
+		Status:               inv.Status,
+		GameID:               inv.GameID,
+		ExpiresAtUnix:        inv.ExpiresAtUnix,
 	})
 }