A transcript can now be shown four ways: plain prose as before, timestamped lines, or as a subtitle file in either of the two common formats.
In the timestamped view every line's time is a link that opens the video at that moment, so a half-remembered sentence leads straight back to the part of the video it came from.
Anything on screen can be copied as before, or downloaded as a file named after the video.
Captions were always timed; the app used to throw the timings away when it joined the lines together. It keeps them now, so nothing extra is fetched to do any of this.