While Azure Communication Services does not support this functionality out-of-the-box, this is something that is on our list of things to investigate for the future. If you have more feature requests or feedback, please file an issues on our github, we would love to hear more about your scenario and how recording would be useful to you! https://github.com/Azure/Communication/issues
That being said, Azure Communication Services is a platform that enables you to build this type of functionality on top of our services. You could try seeing if any APIs offered in Azure Media Services might fit your needs?