A few lines of Javascript in the console can copy that to the clipboard for you. Maybe someone's packaged that up already. (It's on my todo list to look around...)

Control Panel for YouTube [1] has an option to add a new "Download" item to the menu in the video Transcript box (which I've just noticed is currently broken, as YouTube must have changed the implementation again recently)

Here's a fixed version [2] - run this when the transcript is open and loaded.

[1] https://soitis.dev/control-panel-for-youtube

[2] https://gist.github.com/insin/cb938324866c511066bcabe230b6a6...