Record audio in video
I came across the same problem when we went to online teaching after SARS-CoV-2 hit. I found a free workaround, but there are subscription services that work. I can't say for sure that this is the best way to do it (just best for right now?):


Open a web-conferencing app like Zoom, WebEx, GoToMeeting, etc., and start a meeting without others.
Share your screen in the meeting, focussing on the video you want to record. Make sure you select to "Share computer audio" in this step. 
Now open your preferred screen-recorder such as Screencast-O-Matic, Canvas Studio, Echo360, etc. (I don't know if the built-in recorder works), and record the shared web-conference video. 


I hope this was helpful, but I look forward to better options if anyone has any! Good luck!