Use the Crisp Chat JavaScript API to send an event to GA via MonsterInsights gtag version.

crisp-ga-send-event-gtag.html

<script>
	// Send an Crisp Chat event via gtag.
  	$crisp.push(["on", "chat:initiated", function() { 
		__gtagTracker('event', 'Test Event', {
      			'event_category' : 'test_event',
	    		'event_action' : 'test_action',
			'event_label' : 'This is a test event.'
		});
	}]);
</script>
<!-- Add to head section of page using proper enqueue
     techniques or a plugin like Insert Headers and Footers. -->

I have also add these events for better testing:

chat:opened

message:sent

message:received

Update: It seems that events starting to appear on my analytics. Il let you know the next days how its going.