I wonder how to best implement such a feature. I guess users would need to generate public and private keys to encrypt/decrypt messages. Twitter would provision

I wonder how to best implement such a feature. I guess users would need to generate public and private keys to encrypt/decrypt messages. Twitter would provision these keys, but the user needs to save the private key in their own safe storage. But that is unreliable and access to older messages might get lost. How is this usually solved? Is the private key further encrypted with the password of the user and stored on Twitters end? What are the recovery options? No idea how it commonly is best implemented.