What control a managed bundle provider has over their bundle when a bundle is no longer being used? Could a bundle provider remove custom records and/or custom fields we've added to their custom records? We're only concerned with keeping the data in the bundle's custom records/lists

Technically they have full control over it. The reality is that they never do do anything (I've seen multiple bundles we no longer use/pay for and all of them are just sitting there, years later). Now they definitely don't have control over your stuff, so not sure how that would work if there were, say, dependencies with linked native transactions. I imagine they wouldn't be able remove anything with dependencies over which they don't have control. Most of them are pretty upfront that the data/bundle itself will still exist in your account, and it's just that certain portions won't work.

The bundle has references to native NS records and also some of our custom records. I wasn't sure if by removing the bundle all the data is removed as well.