The privilege covers communications between president and his advisors. By claiming the privilege, Trump is stating the redacted portions deal with conversations involving him...
If it IS communications between him and advisors, Barr lied under oath as to the motive of redactions..
Either Trump is falsely using executive privilege to cover up information from Congress, OR Barr perjured himself about the reason he redacted and the material redacted involves direct conversations between Trump and advisors.