Google Meet Transcripts by Scribbl will record all of the captions that are generated during a Google Meet call. When the meeting is over a Google Document containing the transcript is automatically generated for you. The best part is that the transcript is time-stamped! The time-stamps make the transcript easier to read and easier to find a section of the meeting without having to read through the entire transcript. The transcript is a Google Document so you can share it just like you would any other Google Document including publishing a copy for each student via Google Classroom.
It should be noted that if you try this extension and it doesn't work the first time, check to make sure that you don't already have another caption-saving extension enabled in Chrome. If that's the case, disable the other one before running Google Meet Transcripts by Scribbl.
Google Meet Transcripts by Scribbl could be a great tool for teachers who want to have a written record of what they said and what their students said during an online class meeting. (If you record students' comments make sure you are in compliance with your school's policy about recording). It could also be useful for recording the notes or minutes from a staff meeting that is held in Google Meet.
On a related note, here's what I look for when trying new Chrome extensions.