How can I ping or perform health checks on the Cato Socket's WAN interface from the public internet?

The socket WAN interface should block all incoming traffic.
But the socket itself does a lot of last mile checks so you could use that info too!

I would first suggest to look for:
Link health rules:
https://support.catonetworks.com/hc/en-us/articles/4413265629713-Working-with-Link-Health-Rules

Connectivity events:
https://support.catonetworks.com/hc/en-us/articles/360003253057-Monitoring-Your-Site-with-Connectivity-Events

And generate an Web hook alert that can be implemented in your system: https://support.catonetworks.com/hc/en-us/articles/16008675940637-Creating-a-Webhooks-Alert-Integration

You can also have a look at the API integration where you can query our API for the sites status.

There is also an advanced option that you could activate if you contact support but you will not get the same granularity as you will not see all those last mile checks.