Not that it matters to our runaway courts, but the death penalty has been around since our founding. So it clearly doesn’t fall under what they meant by “cruel and unusual”.
In earlier days most executions were public.
Not because the public were ghouls but making the execution public the community could SEE that justice had been served.
Secondly it gave would be bad guys pause to consider the possible consequences of future actions.
Call it a win, win, win.
That just means its not unusual, cruel is a more subjective term.
Honestly the 8th amendment was never meant to apply to the States. And no law long established(since founding) can be ligitimatly held unconstitutional by any court of law.
Of course today we have a court of imagination not law.