Option to disable "Reply to email" callout / Messenger-only support without email forwarding

I’d like to have Messenger-only support setup - the ability to completely disable email forwarding without sending outbound email notifications that prompt users to reply via email (the followup-emails when users miss replies).

Alternatively, I want a setting to disable or customize the "Reply to this email to respond" callout in the email notifications.

This is important because forcing email forwarding as an active channel makes it impossible to run a clean, modern web-based support flow without keeping email open.