January 20th is Inauguration Day for the president and vice-president. The newly elected senators’ and representatives’ terms have already begun. They were sworn in on January 3rd. That’s how Congresspeople who were just elected in November were able to speak in the debates last night.
“On January 3, 2021, the U.S. Senate will convene to open the 117th Congress. The Senate typically operates according to long-standing rules, traditions, and precedents, and the first day of a new Congress is no exception. The Constitution mandates that Congress convene once each year at noon on January 3, unless the preceding Congress designates a different day.1 In odd-numbered years, following congressional elections, a “new” Congress begins. . . .Regardless of the change in date, the first day of a new Congress for the Senate follows a well-established routine. . . .The day begins with the opening prayer and recitation of the Pledge of Allegiance, followed by the swearing-in of senators-elect (and sometimes appointed senators), the establishment of a quorum, notifications to the House of Representatives and the president, and often the election of a president pro tempore and other officers.”
https://www.senate.gov/artandhistory/senate-stories/when-a-new-congress-begins.htm
https://en.wikipedia.org/wiki/117th_United_States_Congress