What a handshake tells you
It indicates that the peers exchanged the information needed to establish their encrypted relationship at that time. It is different from a desktop window opening or an interface being present.
What it does not settle
Traffic still needs appropriate allowed IPs, routes, forwarding and firewall behavior. DNS and IPv6 can follow paths you did not intend. Verify internet access and the expected external address rather than treating one signal as the entire test.
Make the check repeatable
Record the device, network, endpoint and time of the test without sharing private keys. Check recovery after a network change and a gateway interruption. Keep these checks separate from the website’s coarse agent heartbeat.