By Foo Yun Chee BRUSSELS (Reuters) – Online travel agency Booking Holdings Inc’s 1.63-billion-euro ($1.7 billion) bid for Sweden-based Etraveli Group faces a full-scale EU antitrust investigation, people familiar with the matter said. Booking announced the proposed acquisition of private equity firm CVC Capital Partners-owned Etraveli in November last year. Etraveli offers search, booking and fulfilment services of flights through its consumer brands Gotogate and Mytrip and also operates airline integration company TripStack. The European Commission, which has been assessing the deal since Oct…