Unfortunately, none of the Mastodon applications have a separate button for private messages. Formally, the "Direct messages" button is available in several applications. However, this is a standard input field for all messages where you need to mark with a special icon that you want to send a personal message that only the recipient can view. This is inconvenient and during intensive correspondence you may forget to mark “Only for the addressee” when sending the next message.

I want a simpler and clearer interface like in the Jerboa or Infinity for Reddit applications. However, no one is engaged in such development. All Mastodon applications are similar to one another to one degree or another.