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/lobby/invitations.go

@@ -159,17 +159,18 @@ func (svc *InvitationService) invitationSummary(ctx context.Context, inv Invitat
 		gameID = inv.GameID.String()
 	}
 	return notify.InvitationSummary{
-		ID:              inv.ID.String(),
-		Inviter:         notify.AccountRef{AccountID: inv.InviterID.String(), DisplayName: name(inv.InviterID)},
-		Invitees:        invitees,
-		Variant:         inv.Settings.Variant.String(),
-		TurnTimeoutSecs: int(inv.Settings.TurnTimeout / time.Second),
-		HintsAllowed:    inv.Settings.HintsAllowed,
-		HintsPerPlayer:  inv.Settings.HintsPerPlayer,
-		DropoutTiles:    inv.Settings.DropoutTiles.String(),
-		Status:          inv.Status,
-		GameID:          gameID,
-		ExpiresAtUnix:   inv.ExpiresAt.Unix(),
+		ID:                   inv.ID.String(),
+		Inviter:              notify.AccountRef{AccountID: inv.InviterID.String(), DisplayName: name(inv.InviterID)},
+		Invitees:             invitees,
+		Variant:              inv.Settings.Variant.String(),
+		TurnTimeoutSecs:      int(inv.Settings.TurnTimeout / time.Second),
+		HintsAllowed:         inv.Settings.HintsAllowed,
+		HintsPerPlayer:       inv.Settings.HintsPerPlayer,
+		MultipleWordsPerTurn: inv.Settings.MultipleWordsPerTurn,
+		DropoutTiles:         inv.Settings.DropoutTiles.String(),
+		Status:               inv.Status,
+		GameID:               gameID,
+		ExpiresAtUnix:        inv.ExpiresAt.Unix(),
 	}
 }