An address is not a working path
Treat addressing, routing and application reachability as separate checks.
Start with local state
A global IPv6 address says that an interface has an address. A default route gives a direction for packets. Neither observation proves that a remote application will accept a connection. Source selection, filtering and the return route still matter.
Test the service you need
ICMP, a TCP handshake and an HTTPS request answer different questions. Record which one was tested. A successful HTTPS request with certificate verification is stronger evidence for a web service than an unanswered ping, but it still does not measure sustained throughput.
Keep the two address families visible
Measure IPv4 and IPv6 independently when investigating a failure. Record the actual remote address and the source interface. Automatic fallback is helpful for visitors, but it can conceal which path succeeded during diagnosis.
Look beyond initial connectivity
If a connection opens and large transfers stall, inspect path MTU, loss and filtering before blaming an application setting. Preserve the original state and make one reversible adjustment at a time.