Importantly, the word archive gives a sense of messages or records orLikewise, I prefer the word Archive because of two implications the word carries: shared and permanent.
But I may be overreacting to a few instances (reported in the Yahoo Groups moderator groups YGOG and GMF) of novice moderators ripping through the Messages, deleting as they read them because they thought that was a kind of personal inbox.
Speaking of which maybe, and especially when a user clicks through to a message from "Your Inbox", it may make sense to put a more explicit warning on the Delete function. Perhaps "Are you sure you wish to delete this message from the Message Archives of GROUPNAME? This cannot be undone."
The problem with "Archives" in the Groups.io context is that Files (and future Photos and/or Links) areas are no less Archival in nature than the messages. That's the flip side of others' observation that new members won't expect to find (current) messages there - the word doesn't specify the type of content.
A compromise might be to label them "Messages" in the left column, but "Message Archives" in the breadcrumb bar at the top of the page (where there's more room).