In cloud, I added the following configuration for Kibana:

xpack.actions.enabledActionTypes: []

Here's what the Connector list looks like:

Note that it LOOKS disabled, but it's actually enabled. This is for historic reasons. The connector should display as enabled and not have the question/circle icon that says "This connector is disabled by configuration" (or similar).

If anyone lands here because they REALLY want to disable a pre-configured email connector, you can use the following configuration which essentially does not allow any emails to be sent (no email address will be valid):

xpack.actions.email.domain_allowlist: []