Yes we do! When you're viewing a session playback, you'll see information about the browser and operating system that the session was recorded on.
If you click on the browser and operating system, you'll be able to view the full user-agent string, which you can then paste into a user-agent string parser available online (such as https://developers.whatismybrowser.com/useragents/parse) to identify which browser and version this user was recorded on.