An impeachment is not a criminal trial, the Supreme Court would have no authority to make a decision in an impeachment.
Impeachment is purely a political tool to remove nefarious actors from the government. So an impeached justice would have his spot on the bench taken away, and then would be a regular citizen who can face trial and imprisonment like any other.
If they decide to ignore that rule, it’s literally the job the of the president to have them arrested and brought before congress to face their impeachment.
I would hope if the court tried to play that hand, congress would actually start using their authority and install a new court, but I trust congress to have a spine as much as I trust my 102 year old neighbor to mow his lawn.
But don’t worry, that would be like the 3rd constitutional crisis we’ve had in 5 years. They’re getting kind of boring now anyway.