Each client has their own media library. You reach it from inside the client's workspace, and the content you publish for that client pulls from it.
Open the client's media
Open the client, then choose the Media tool in their workspace. Media is a tool rather than a report, so it is not tied to a date range. What you see here belongs to that client and stays separate from every other client you manage.
Upload and organize
Add the client's images and assets to their library so they are ready to use. When you write a post in that client's composer, you attach media from this same library, and the preview shows the actual image you picked. Keeping each client's assets in their own library is what stops one client's files from showing up in another client's work.
Access follows your role and scope
What you can do with a client's media follows your role and product scope on that client, the same as everywhere else in the workspace. If Social is not in your product scope for a client, you will not be working in that client's content tools.