It is not obvious that they were there for the same reason. They were delivery boys, toting Davis' ultimatum.
In fact, as the Peace Commissioners were attempting to present the greetings of the Confederacy, Lincoln was sending the Union Navy, secretly, to Charleston harbor.
Where the Davis regime had been trying to starve the fort into submission. Obviously peace was not high on Davis' to-do list.
You said: “It is not obvious that they were there for the same reason (to negotiate peace)”.
Certainly they were. Look them up in any history book. They were called the Peace Commissioners.
Wish that Lincoln could have been known as the “Peace President”.
“Where the Davis regime had been trying to starve the fort into submission.”
You know that that was a contrivance created by the Lincoln administration to give their warship expedition cover from public opinion.