In this case the judicial angle isn’t punishment, but completion

That’s the crazy part, the bare minimum appeal was to change his sentence to life in prison. That would still be an end to the case with a definite ruling. They chose to kill him. A lot of the opposition to his execution wasn’t even asking to release him, but to just change the sentence, they couldn’t even do the bare minimum to spare a (potentially innocent) life. Sheer barbarism.