Before you read the result
What Twingate documents about these signals
The points below come from Twingate's own documentation, which describes the client as matching destinations against an access list rather than capturing everything a device sends.
Only Resource traffic is routed
Twingate documents the client as detecting network connection requests to protected Resources, and states that if the destination address matches a Resource in the access list, a connection is initiated via Twingate to the remote network. Traffic to anything else is untouched. A public IP check run during a Twingate session is therefore reading your ordinary connection, correctly, and there is no tunnel address for it to report.
DNS for Resources is proxied, not replaced
The client proxies DNS requests for protected Resources, forwarding them for resolution to a Connector inside the remote network. That is split DNS: private names resolve on the far side, public names resolve the way they always did. A DNS leak test asking about a public domain is measuring the second half of that arrangement, which is the half Twingate deliberately leaves alone.
DNS over HTTPS is a separate switch
Twingate documents native DNS-over-HTTPS for users running its macOS, Windows or Linux clients, and states that it encrypts all DNS traffic regardless of the originating application with no configuration changes required. That changes what a resolver check can observe about this device, so it is worth knowing which state you were in before you read one.
Filtering happens at resolution time
Twingate's Internet Security features include DNS filtering, which decides at resolution time whether a name is answered at all. A page that will not load during a check may have been filtered rather than blocked by a network fault, and those are different findings that a single reading will not separate for you.
Comparing it with a consumer VPN misleads
Twingate publishes its own comparison against traditional VPNs, and the difference is the point. A consumer VPN is judged by whether your visible address changed. This product is judged by whether a named Resource became reachable to the people entitled to it. Reading one result with the other's expectations is the usual route to concluding that something has failed.