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.