Microsoft is still working to bring its new Skype experience, or Skype v8, to the same level of functionality as previous iterations of the app. The latest update for Insiders on desktop brings back the ability to see your in-call chat and the conversation list at the same time.
Basically, if you're on a call, the chat panel for that conversation has now been moved to the right side of the screen, which leaves the left side free to display the conversation list. What's more, the chat panel in a call can now be resized to fit your preferences. Also, as a result of moving the chat panel button to the right side, the call snapshot feature has been moved to its place on the left side of the screen.
Skype classic already let users see the conversation/contact list and the chat at the same time during a call, though the call section and chat were split vertically instead. If this is one of the limitations that's been holding you back from adopting the latest version, this may be good news for you. If you're using Skype on mobile devices, the call experience has recently seen some changes there too.
Microsoft has been making improvements to Skype on a frequent basis, including new (kind of) customizable emoticons. If you're interested, you can download the Skype desktop app here for either Windows or macOS, or grab the Windows 10 version from the Microsoft Store. You'll need to go to the app settings to get Insider builds, but the new feature should make its way to all users in the near future.