I suppose James Baker is going to be a key figure of this earlier George H.W. Bush administration.
Yes, he certainly will. He will stay on as Chief of Staff. Bush gets a break here: he gets both continuity and loyalty. The shake-up will be at lower less visible levels, which is good for Bush. Baker is still regarded as the gold standard in running a White House, so organizational issues won't be a problem. Much of what went wrong for Reagan in the second term flowed from Baker leaving that job and moving on to Treasury.