hmm... I am from a small town so we have a jail for trial and only after sentencing to prison. LA may be different.
Burt calls it "Federal" I would think he would be state prison not Federal.

Just as a geeewiiiizzzzz, When Lizzy asks if Saul went to Eastern Bay, (and we are back to Burt lol) says it is Federal and Saul would not be sent there

That may be true or not. I do not know. But I know Saul did not deny it.

In Chapter 1, Angel brings up the idea of prison and that he could hang out in a cell. He also notes "And I know you could to". He has to be speaking to Michael or Saul. So, does Angel know that Saul went to prison. Are the waivers held in a personal file? Would Angel have access to it? Saul says he never told Michael. If Saul did not tell Michael with the time they have spent together (including simultaneous tours overseas) I do not think Saul would tell Angel.