Looking for a way to share access rights to Files to some colleagues but disable their access to see the conversations. Is there a way to grant specific privileges to members or once you've added someone as a member they can see everything?
Yes, because Teams is backed by SharePoint with Files and SharePoint has it's own permissions all you need to do is use the "Open in SharePoint" link on your files tab, then you can highlight the content you need to Share with others and Share it. If you require anonymous guest link access you will have to have you or your admin run set-sposite -SharingCapability command to allow guest external sharing for your site.
You can also directly add people to your SharePoint site (Not choosing add to group, but add to site) if you want them to have access to everything.