Would you resubmit a research paper after it has been superseded by another as yet unpublished paper?

This is a tricky situation, though just one spin off of the current absurd state of academic publishing, and particularly the preposterously slow and uneven peer review process in math. My personal feeling is that you should try about as hard to get paper A published as you would any other paper (though strategically, I would probably submit to a somewhat less selective journal). It does feel a little silly; I actually now am in the doubled version of this situation, where I wrote a paper, wrote another that superseded it, and then wrote another that superseded that one, all of which are under review simultaneously at the moment. The process in mathematics has gotten a bit silly just generally, but any reason you had to publish paper A before (whether it is padding your CV, making sure that it is regarded as a reliable part of the peer reviewed literature, or hoping to get useful feedback from a referee) is equally in force now, so I don't see what has really changed.

Yes, you should resubmit. Research is a journey, and having both papers published creates a record which can help others who are tracing the steps of your journey.

There is nothing unethical in resubmitting your rejected paper to another journal. If you wrote a paper B which contains a stronger result, and does not use the result of A, you may of course decide not to publish A. But if you feel that A still contains something interesting which is not in B, re-submit it. However there is a chance, that the new referee of A will know about B, and recommend to reject A.

The situation becomes even more complicated if B is not your paper but of someone else. In which case you may loose the priority. An excellent remedy against this is posting on the arXiv all papers before you submit them.