The only current method that I know of to search the complete content (site, mailbox, and notebook) held for a group is a content search executed through the Security and Compliance Center. This does not take into account plan metadata belonging to a group or any team chats created in a team associated with a group, but content searches will find the other data. Of course, you can't have everyone going to the SCC to launch content searches, but I just wanted to point out that this is how you could do it.
The searches launched by OWA and Outlook focus on the content of group conversations, including any attachments within those conversations.
