I'm not sure if the original question was about Confluence Cloud or Server, or if it was about building support for Team Drive into Confluence itself. But for anyone who's using Confluence Cloud and open to using a plugin, I would highly recommend Google Drive & Docs for Confluence. It does support Team Drive.
FYI - this is not an Atlassian issue, this is a Google issue. The Google File Picker API does not support Team Drive at the moment, only Drive. (That's why files in Drive works and Team Drive doesn't.) So until Google fixes their API, third-party products like Confluence, Trello, Draw.io, Asana, etc. will not be able to pick files from a Team Drive location.
If this issue is important to you, please click the "star" at the top of Google Issue 36761624 so it gets re-prioritized.
Thanks Eileen for the link. The latest comments there (after your post here) indicates the newest file picker API includes Team Drive support now.
https://issuetracker.google.com/issues/36761624 - Comment #13
"Isn't that already supported? I am under the impression that it is https://developers.google.com/picker/docs/reference#DocsView - DocsView.setEnableTeamDrives(boolean)"
Let's hope is easy for Trello and the other app developers to get it working.