Ten affordable housing developments worth more than $263 million were among the first recipients of a round of competitive state grants and loans announced Thursday by Gov. Dannel P. Malloy. The multifamily developments, representing 1,018 units — with at least 367 to be leased at below-market, affordable rates — include three in Bridgeport and one in Norwalk. Most of the projects are eligible for up to $5 million each in state support. It’s part of a 10-year, $500 million effort to foster so-called workforce affordable housing throughout the state that was previously approved by the General Assembly. The state money is designed to bolster private financing for the projects.