In my profile page, can I revert back to the screen before I selected
Track My Next Privilege?
I understand what you want, but the new profile tracking functions are specifically for "tracking" things, and you cannot track an already earned privilege.
As you stated, there are already multiple other methods to see your current privilege status.
Even though the function does show the currently earned one, I don't think it's designed to do this specifically as an option to show your current level. More to show the one you've just earned because it's the natural thing to do before you choose which one to track.
It's probably pride or something
I really wouldn't worry about that. Anyone who in anyway sees anything negative from your current rep/privilege level simply does not warrant/deserve your concerns.
Decent people do not view or judge you based on your rep level.
Besides, people will know what your current privileges are without even going to your profile - from the rep you have shown all over the site in your question/answers/etc.
The concept resembles other features, like voting, which give a
certain period of time before a choice becomes permanent.
True, but voting is substantially more important, given that voting affects other users rep, their answers being moved up, or down or even hidden, etc.
I'm not against what you want whatsoever, and is technically possible, but it is dev time, and for that it really needs to be worthwhile - how many users would use it, how useful it is, etc.
The grace on voting is quite important to have, whereas your request is a little more "personal" and not essential in any way.
Rather than "undo" the action, you could raise a new feature-request asking to be able to permanently choose to show either "track next" or "show current".
This will likely be seen/used by more users, and is a bit simpler than an "undo" function. It's just a clear option which is always there.
Although, I'm not sure if this or an undo option would be implemented as the function is for "tracking next" not "showing current".
Worth a try, though :)