The professor has accepted me to be is RA, but we had initially agreed that I should apply for Fall 2022. Now he suggested "You may wish to apply for the summer 2022 session if you can manage that." I don't want to apply for summer 2022 to have adequate planning time. How can I best respond to this request?
If you are going to work with your professor you will be communicating with him. So why not start communicating openly right now?
Find out why he would like an earlier start; explore why you might find that difficult or not; come to an optimal solution for you both.
If you can do this honestly and cooperatively, it augurs well for your future working relationship.