A question about DN 23 and existence of soul
You wrote ...


  (Payasi argues there is no soul so no afterlife.)
  
  However, Kassapa, one of the principal disciples of Gautama Buddha, argues there is a soul.


... but I don't think so. Instead I think the dialog or argument in the sutta is:


Payasi: there is no afterlife because we don't see a visible soul leaving the body at death
Kassapa: the existence of a visible soul is not necessary for there to be an afterlife (for example when you dream there's no visible soul living the body) -- the non-existence of a visible/separating soul doesn't prove there is no afterlife


That (saying "the existence of a soul isn't necessary, and needn't be assumed") is not the same thing as saying "there is a soul".
The main argument is about "afterlife", it is not about "soul".

Secondly the argument in Pali uses various words like:


  
  āyu
  life; vital power; duration of life, life-time; long life.
  jīva
  


Those words are used in several suttas -- in MN 63 for example, where various questions about the body and soul are declared to by the Buddha to be "not declared":


  And why haven’t I declared these things? Because they aren’t beneficial or relevant to the fundamentals of the spiritual life. They don’t lead to disillusionment, dispassion, cessation, peace, insight, awakening, and extinguishment.


Thirdly, even if Buddhist doctrine did say that something like that existed, and if someone translated that statement or that word as "soul", I'd try to doubt whether the word "soul" there has the same kinds of meanings as is taught by other religions