My own TBR is just a google sheet of every book I own that I haven't yet read. Some of those I don't want to read and will never read, so calling it a TBR is not strictly correct (and there are books I do want to read which I don't own), but the thing I am interested in tracking is my unread books. Whenever I try to filter out the things I don't think I'm likely to read, I quickly run into edge-cases where I'm not sure, and it becomes a bit of a futile exercise.
Or, in other words, you can manage and track your To-Be-Read list however you like. It only really matters to you.
Regarding Calibre, I believe you can split your collection into many separate named libraries and switch between them at will. And you can add custom columns to the list of books for whatever extra information you like. Personally, I haven't customised calibre and I only use it for my non-kindle ebooks, so it's only a small part of my overall collection.
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