When adding a new field to an existing field group that belongs to a post type with many existing posts, how do we fill that new field with some sort of default data for all the existing posts?
There is no way to add a default value to a field for existing posts.
You would need to write a script you run once to populate the database (you can add a code snippet at Toolset > Settings > Custom Code and run once, rather than activate).
You would need to get all the posts of the type in question (using get_posts), the loop over the posts and for each one use add_post_meta with the unique attribute set to true to provide a default value, while not overwriting existing values if they exist.
That sounds like a big ask for people who don't know how to code.
I'd like to make a feature request that when adding new fields, we are provided a text field where we can enter default data that will be inserted into that field in all pre-existing posts.