Is your feature request related to a problem? Please describe.

Yes. When sending a conversation reply via the REST API (POST /api/v1/accounts/{account_id}/conversations/{conversation_id}/messages), Chatwoot automatically triggers an outbound "conversation continuity" email to the customer if they have an email address on file and are marked offline.
Currently, there is no way to suppress this email on an individual message level. The only workarounds are to globally disable the email continuity feature at the account level via the Rails console, or perform a complex "Delete-Post-Restore" sequence by temporarily stripping the customer's email address via the API before sending the message. This introduces race conditions in high-concurrency environments and complicates automated workflows (e.g., sending silent diagnostic data, automated receipts, or system-triggered notes that customers shouldn't be emailed about).

Describe the solution you'd like

We need an optional boolean flag such as skip_continuity_email available inside the POST messages API request payload.
When this parameter is explicitly set to true, the API should prevent the background job worker (Sidekiq) from queueing or executing the outbound conversation continuity mailer for that specific message, while still rendering the message inside the dashboard and widget normally.
Proposed API Payload Example:

{
"content": "This is an automated system response that should not trigger an email notification.",
"private": false,
"skip_continuity_email": true
}

Describe alternatives you've considered

1. Using "private": true: This prevents the email from being sent, but it also hides the message from the customer on the live chat widget entirely, which breaks use cases where the customer should see the message in-app, but shouldn't get an email ping.
2. Stripping the contact email address: Modifying the contact schema via API right before sending a message and restoring it afterward. This creates messy database updates and breaks webhook integrity.
3. Disabling continuity globally: This is a blunt instrument that stops valuable continuity emails for legitimate human-agent interactions.

Additional context

This feature would greatly improve Chatwoot’s flexibility as a headless or hybrid CRM backend, allowing developers to fine-tune the notification experience for automated bots and programmatic system replies.