Just pressing ⌘+S in Terminal already saves the complete output to a text file. It does not preserve colours though. See below for a short output example.
Last login: Thu Oct 14 19:42:28 on ttys000
gerwin@Gerwins-MacBook ~ % pwd
gerwin@Gerwins-MacBook ~ % cd /
gerwin@Gerwins-MacBook / %
I can advise you on the Movavi program https://www.movavi.com/screen-recorder/. In this program you will do everything that you need, here everything is simple and easy, very light and simple interface!
I get a partial answer from ShareX's solution on GitHub:
I have tried add date taken for jpg using exiftool as follows.
exiftool -overwrite_original '-DateTimeOriginal<FileCreateDate' DIR
Thus one trick for doing the task using ShareX is through After capture tasks -> Perform action, with exiftool and arguments as follows.