The SCOTUS itself plays no role in impeachment or its trial. Impeachment is the sole preserve of the HoR and the trial is conducted in the Senate. During impeachment of the President the Senate is presided over by the Chief Justice (presumably to avoid a conflict of interest if the VP were presiding. Remember under the original rules the VP was the man who came in 2nd). The House can impeach for anything it wants and claim it is a high crime/misdemeanor.
Democrats have been talking about impeachment since November 2016. Their latest ‘crime’—a withholding of funds to Ukraine is just the latest in a long line of terrible things that PDJT is or has done. It really does all boil down to Orange Man Bad.