iOS: can one pause a screen recording for continuing it later? Can one pause a screen recording and then continue it? There is a related question for macOS. My question is for the default screen-recording of iOS 13. If the answer is negative, is there some free apps which are able to do it?
I have not heard of any way to do that, nor any 3rd-party app that can do it.

Your best bet would be to find an app (or Shortcut, possibly) which can merge multiple videos together, and then you could run that after taking 2 or more.