This is a good question and I would like to share some useful insights to prepare to what's mentioned above:
What personality traits are most important to demonstrate with the partners:
Better synthesis – Your analytical mindset has already been tested in earlier rounds. Partners would like to test your client readiness. Partners pay more attention to how you draw your conclusions, communicate your conclusions, how you synthesis etc.
Comfort with less structured case discussion – Partners love to test your creativity, out of the box thinking. Multiple times in the discussion they can ask you your opinion on the data point/clarification that you had asked, to check your business acumen e.g. you asked, what is the growth rate of our client; partner responds what number would you want to assume? or open-ended questions e.g. tell me more, is there anything else?
Consistent stories and deep dives – Partners would want to know your story. They want to see whether your decision to join McKinsey is consistent with your career story. Whether the achievements you have mentioned on the CV are consistent with your project stories. Partners will drill down into your experiences and achievements to the extreme. They want to understand how you react to challenges and how you think and communicate about your past work.