BUG: pd.NA showing up as NaN in Categorical repr
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I have been thinking about a change to the use of the na value in `Categorical`, and just wrote up #52687 after being reminded by this PR. This would also change the repr IMO as a consequence of the change, so I  think that would make this PR unnecessary,. Sure, happy to see what you got. 

Feel free to take my test(or any parts of this PR) if you need it. This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Looks like this has gone stale. Closing to clear the queue but feel free to reopen if you want to continue FYI, there is a slightly related #53190, which isn’t getting traction though…