I don't see an id in either console or central. Is this what your UI looks like or am I missing a setting?

Finding via Consul or Central might be version dependent. In the SDK there is a db object to get this information: https://docs.q2developer.com/docs/guides/notifications/secure_message.html using the message recipient group db object: https://docs.q2developer.com/docs/api_references/q2_sdk/db/db_objects/message_recipient_group.html#module-q2_sdk.hq.db.message_recipient_group However, this is not currently not available via Caliper API. You could make a custom endpoint to do this functionality, but that might be a bit overkill.
If you have access to Q2 Central you can find it there. Navigate to Manage Secure Messaging under the Administration menu tree. That should show all your Secure Message group names and GroupID. That's where I had to look.
Click the Feild Chooser and then select GroupID