As he tries to secure a modicum of relevance for Democrats in the Florida Senate, and chart a political future for himself, state Sen. Jason Pizzo is doubling down on a centrist message — and seeking distance from the party’s progressive wing. Pizzo is at the beginning of a two-year term as the leader of the small band of Democrats in the state Senate — 12 out of 40 senators — with Republicans holding such a large majority they can implement anything they want. Pizzo began his tenure as Democratic leader with warm words for the Republican Senate president, a pledge to work cooperatively with the majority party, a plea to be treated fairly — and some notable criticisms of fellow Democrats, nationally and at home. Under the approach Pizzo outlined, woke is out, identity politics is out, and progressive policies are out. Florida Senate Democrats aren’t the kind who fit the caricature he said Republicans like to draw.