Just to say the fact they wish to impeach after his presidency is not relevant.
Its not a criminal trial...the point is to decide whether he will have the right to hold office again. The constitution makes no mention of the timing of an impeachment and subsequent trial This makes sense because it takes time to accrue evidence and an office holder could commit “treason, bribery and other high crimes and misdemeanours” in his last few days in office, for example, thus escaping justice by simply resigning the day before the trial (or even during).
Once he has left office a president is also no ordinary citizen, either. He remains an ex-president, is addressed as a president and is entitled to the benefits, financial and otherwise, of that office for the rest of his life. This includes the right to certain security briefings etc. Then there is precedent. Congress has begun impeachment trials on officials who left office on three separate occasions. Just because these men were not presidents is irrelevant, since there is only one impeachment clause that every official is subject to.
whether the facts are such that Trump should be subject to impeachment is another matter but that President Trump has left office does not mean he is no longer subject to conviction.