Feature Request: Better Error Logging

The Q CLI will frequently give an error like

```
“Amazon Q is having trouble responding right now:
0: dispatch failure (io error): an i/o error occurred: error sending request
1: dispatch failure
2: io error
3: an i/o error occurred: error sending request”
```

which is not clear, but, in the qchat.log file there will be a much better error like,

```
[2m2025-07-31T14:12:06.569208Z[0m [31mERROR[0m [2mchat_cli::telemetry[0m[2m:[0m [2m519:[0m Failed to post toolkit metric [3merr[0m[2m=[0mdispatch failure: io error: an i/o error occurred: error sending request (DispatchFailure(DispatchFailure { source: ConnectorError { kind: Io, source: CallError { kind: Io, message: "an i/o error occurred", source: Some(reqwest::Error { kind: Request, source: hyper_util::client::legacy::Error(Connect, ConnectError("dns error", Custom { kind: Uncategorized, error: "failed to lookup address information: Name does not resolve" })) }) }, connection: Unknown } })) [3mmetric_name[0m[2m=[0m"amazonq_messageResponseError"
```

Which clearly shows that there was a DNS Error occurring.

The ask here is to improve the error handling so that the root error is surfaced without the customer having to log dive.

Beginne damit, den Fehler in der Q CLI zu reproduzieren und die für Benutzer sichtbare Meldung mit dem entsprechenden Eintrag in qchat.log zu vergleichen. Verfolge, wo der protokollierte Root-Fehler verfügbar ist, und definiere den Abschluss so, dass die zugrunde liegende Ursache, etwa der DNS-Fehler, angezeigt wird, ohne dass Kunden qchat.log prüfen müssen.

Vom Indexierungsmodell aus dem Issue-Text verfasst.