Twitter has now started rolling out encrypted direct messages, but it is currently not easy to have fully encrypted conversations on Twitter.
Firstly, only Twitter Blue users and verified organizations have access to encrypted direct messages on Twitter for now. Since both parties involved in a conversation need to have support for encrypted messages, it means that only Twitter Blue users and members of verified organizations can have encrypted conversations with each other.
There is also no support for sending any type of image, video, or other media in the encrypted direct messages on Twitter. Lastly, it appears that the encryption is not entirely 100% secure. For example, message metadata is not encrypted, and they do not have protection against so-called man-in-the-middle attacks, as reported by Engadget.
The conclusion one can draw is that, for now, it may be best to refrain from having private conversations that you want to keep confidential on Twitter.
