User-to-user interaction can be limited to chat by disallowing PMs by removing groups from the personal_message_enabled_groups site setting. Then only staff will be allowed to initiate new personal messages, while most users won’t.
But while chat is a plugin and can be disabled entirely, PMs are a core Discourse feature and some actions rely on them where you cannot replace them with chat. For example, when you flag something and enter a reason, that creates a personal message. Or when you export your user data, the link for the download is sent as a PM. So you cannot fully disable them as some Discourse features use them