You will enter Schengen to retrieve your luggage, then check it back in with BA. You then go through security (about 75 paces from the BA desks) and can then freely roam the lounges and restaurants. You will then exit Schengen near the gates BA uses. So yes, you'll show your passport twice. Not to be pedantic, but you don't have a connection, you have two unrelated flights with all the non-protection this entails.