Re-watching the message I don’t think the average viewer would get the impact of what was happening or who was saying it right away just from the two lines “day of revenge, day of the Sith”. I think it would be more obvious that it’s Palpatine and more impactful for the audiance and the trilogy as a hole if the first part “the work of generations is complete” and “the great error is corrected” were included. Only thing you’d have to do is play the extra lines over Rey and Leia’s reaction, which I think works better because that way the audience’s reaction bounces off the characters’ reactions to hearing his voice.