Does Apple have its own Swift (or, at least, Objective-C) server-side framework
with similar capabilities like Vapor or Kitura have?
I'm not interested in using third-party frameworks or Cocoapods.
Any help appreciated.
Vapor and Kitura are both build on Apples Swift-NIO.
So you could technicaly go with that as well but you would have to build alot of functionality by yourself that frameworks like vapor and kitura bring, to make you life easier.