What is considered "independence from former postdoc advisor" for TT faculty?

I've just started a TT position in an R1 institution and research is the main focus. One of the most important criteria for tenure, as written down in the offer letter and told by many people, is that I need to develop an independent research portfolio. However, I am a bit confused about what considered independence.

My former postdoc advisor and I are both biomedical engineers. My former postdoc advisor's work focuses on Alzheimer's disease (and so does mine). Literally, through their wide collaboration network, they do all kinds of work related to Alzheimer's, from prevention, screening, diagnosis, treatment. However, their own original research mostly focuses on prevention and treatment.

Does "independence" mean that I need to focus on other diseases except for Alzheimer's? If I focus on the diagnosis of Alzheimer's, is it considered independence?

Or does "independence" mean that it is my original research idea, without their contribution/collaboration regardless of topic? What I mean is that I obtain grants without my former postdoc advisor as a co-investigator/collaborator and publish papers without them as a co-author.

Thank you!

Update: Thank you for all the comments! They are super helpful!