They were sent to the Chief of Staff while he was in the performance of his duties.
Biden declined to shield them under Executive Privilege. Which will have pretty bad consequences when a Republican is again President.
But the issues are 1) Are the messages factual (not fake)? 2) If not fake, what time were they sent? 3) When did President Trump issue his statement?
That is what the media will focus on, not if they were private.
We have on record Trump ending his Jan 6 speech telling them to protest peacefully. That alone is way more than he would be required to do.