Today chrome://media-internals is a singleton in the browser process. So players from all user profiles show up in chrome://media-internals page. For example, if I open chrome://media-internals using my personal gmail account/profile, I am able to see what video I watched using my corp account/profile. It's not a big privacy issue since multi-profile are supposed to be used for trusted accounts. But I was still slightly surprised. Also, from a UX perspective, per-profile media-internals will help reduce the number of players on chrome://media-internals, making it slightly easier to find a particular player you are interested in.

PS: I checked on ChromeOS by switching between two users on ChromeOS and this does NOT happen. Apparently each user has its own browser process.

PS: chrome://sync-internals is per-profile, which makes a lot of sense, since sync is tightly related to profiles/accounts.