But I don't immediately believe the link that 'car culture' -> 'earlier cognitive decline'. Car culture, for example, is usually associated with living on larger plots of land, which comes with its own set of tasks and chores that can keep someone older occupied. A smaller apartment requires much less ongoing work.
I think a lot depends on the individual and how they best stay active. More dense living probably provides easier opportunities to do things, whereas less dense living sort of forces you to perform ongoing tasks.
There is a relevant concept in psychology called activation energy, James Clear provides a good introduction to it. Certainly in recent years screens seem to be incentivizing more stay at home behavior. People used to not own a TV, many quite intentionally, before our other screens were invented. But it is a very complicated topic.
It's simply much easier to walk to a coffee shop, or park, or wherever for those who have maintained their mobility (probably in part by living in a walking-centric environment) than it is to hop in a car, sit in traffic, for small things. It's less of a barrier.
There's plenty of places where a car is not necessary and even if people think a car's necessary I'm often the only one on a bicycle in many places.. It's doable if you're willing to put in the effort.
It is. But looking ahead, knowing what we know now, choosing to age in a car-centric place comes with known health effects.
You can choose to live where you don't need a car, but those places become fewer and fewer because of the distances needed for cars. (as in parking space minimums mandated by the city).
"Not just bikes" on Youtube goes into this a lot. Car-centricism is self-reinforcing. Eventually you have no such thing as a mid-density neighbourhood.