WASHINGTON—The U.S. Senate on Monday confirmed former union leader Marty Walsh, a son of Irish immigrants, as the next labor secretary. His confirmation, by a 68-29 margin on Monday evening, is likely to have a major impact on U.S. workplace laws and regulations as he looks to further enforcement of occupational safety and health rules, overtime payments, and the administration of employee benefit plans. Walsh, 53, led Boston’s Building and Construction Trades Council for two years before winning the 2013 race for mayor with strong backing from large labor groups. He has also served in the Massachusetts House of Representatives. Walsh has supported key proposals affecting workers, including a $15 minimum wage, paid family leave and the PRO Act—a proposal to update labor laws and give workers more ability to organize at work that the House of Representatives passed last year. “When I was running for Mayor, I was kind …