Additional features, settings, or issues not covered by specific Microsoft Teams categories
I figured out a way to do this!
In New Teams, you have to go to go to the meeting SERIES (if you open one recurrence you will have the option at the top to edit series) and edit the Notes component there.
Anything you put in there will show up in the Notes component for every recurrence.
However: if you just click on the Notes icon during an occurrence of your series, it will create a new Notes component specific to that date. If you want to continue to edit the single Notes component from the series, you will have to use a link to get there instead.