Barry Sternlicht’s Starwood Property Trust Inc. agreed to buy a General Electric Co. energy-finance business for $2.56 billion to expand beyond real estate holdings. The acquisition includes a roughly $2.1 billion portfolio of 51 loans backed by assets such as pipelines, power plants and wind farms, as well as $400 million of unfunded commitments, Starwood and GE said Wednesday in separate statements, confirming an earlier report by Bloomberg. The project-finance debt unit -- and its 21-person team -- is part of GE Capital’s Energy Financial Services business.