Can I "Trace" the Requests Happening Behind the Scenes?

Unfortunately I also do not know a way of tracing OOTB component's API queries, there are a few Angular ones that do AJAX requests directly to the API, those you can trace, but that's about it. Toolbox does only trace custom components, not OOTB ones (at least afaik).

But for the GroupHub message list, a query like this is roughly what you need:

"SELECT ${fields?join(',')} FROM messages WHERE depth = 0 and grouphub.id = '${id}' ORDER BY post_time DESC LIMIT 10 OFFSET 0"