According to a report from Aggiornamenti Lumia, the next feature update to Windows 10, codenamed 19H1 since it's slated to ship in the first half of 2019, will come with a new system app that's made for mirroring calls. The app is similar to Your Phone, which allows you to send and receive texts, and interact with photos from your gallery.
The app is called Windows.CallingShellApp, and since it's not actually active in Insider Preview builds, it's impossible to be completely sure about what it does or how it will work. The data obtained by Aggiornamenti Lumia shows strings that say things like, "Fold the device over to return to call", "Transferred", "Could not transfer", "Show in-call options", "Connect to Wi-Fi to do things that require an internet connection", "You're almost out of WLAN range", and so on.
The path to bringing Windows 10 and your phone closer together has been a long and confusing one. When Windows 10 first launched in 2015, Windows phones were still a thing. In Windows 10 version 1511, Microsoft tried to integrate Skype with the OS for all of your communication needs, with three separate apps: Skype Video, Phone, and Messaging. Those were replaced by the UWP Skype app, but Messaging remains, and it was supposed to integrate SMS with a feature called Messaging Anywhere.
That feature was killed off, and Messaging remains a mostly useless app that comes pre-installed on Windows 10, and one that you can't easily uninstall. SMS integration is coming to Skype, although it's a mixed bag on which versions of the app actually work. But call mirroring is something that we haven't heard as much about.
Hopefully, Microsoft will debut the feature via the Insider Program sooner rather than later, so we can learn more about how it will be implemented.