According to Is the Senate required to pursue a trial if presented with articles of impeachment?, impeachment articles themselves do not expire as written inside Chapter 27, Part A, Section 5 of House Practice which reads:
Sec. 5 . Effect of Adjournment
An impeachment may proceed only when Congress is in session. 3 Hinds Sec. Sec. 2006, 2462. However, an impeachment proceeding does not expire with adjournment. An impeachment proceeding begun in the House in one Congress may be resumed in the next Congress. 3 Hinds Sec. 2321; 111-1, Jan. 13, 2009, p __. An official impeached by the House in one Congress may be tried by the Senate in the next Congress. Manual Sec. 620; 3 Hinds Sec. Sec. 2319, 2320.
Although impeachment proceedings may continue from one Congress to the next, the authority of the managers appointed by the House expires at the end of a Congress; and managers must be reappointed when a new Congress convenes. Manual Sec. 620. Managers on the part of the House are reappointed by resolution. Manual Sec. 604; Deschler Ch 14 Sec. 4.2. Thus, the articles of impeachment against Judge Alcee Hastings were presented in the Senate during the second session of the 100th Congress (100-2, Aug. 3, 1988, p 20223) but were still pending trial by the Senate in the 101st Congress, when the House reappointed managers (101-1, Jan. 3, 1989, p 84). The articles of impeachment against President Clinton were presented to the Senate after the Senate had adjourned sine die for the 105th Congress, and the Senate conducted the trial in the 106th Congress. Manual Sec. 620.
The text above mentions Impeachment proceedings from the house's perspective. It does seem to imply that adjournment does not restart what the house is doing, but simply causes a reappointment in managers. It also mentions that the next Senate may indeed start a trial from articles submitted from the previous house session. However, nothing here mentions the situation of a trial that starts well within the term of one Senate session then goes on into another Senate session. And the possibility of President Trump's Second Impeachment trial starting within one Senate session, but being continued into a different Senate session never happened, since it never started in the 116th Senate, so this situation has never occurred. This leads to my question:
While Impeachment articles do not expire, if a Senate trial starts, but goes into the next Congress, does the Senate have to restart the trial from the beginning?