fix: Track configured auth for turn errors

[benbrandt]

Closes #244

[anvilpete]

Many thanks for this @benbrandt!

I did some quick testing, and it seems to work well.
However, 401 errors look a bit wonky:

{
  "jsonrpc": "2.0",
  "id": 3,
  "error": {
    "code": -32603,
    "message": "Internal error: Reconnecting... 5/5",
    "data": {
      "message": "Reconnecting... 5/5",
      "codexErrorInfo": {
        "responseStreamDisconnected": { "httpStatusCode": 401 }
      },
      "additionalDetails": "unexpected status 401 Unauthorized: Incorrect API key provided: fdsa. You can find your API key at https://platform.openai.com/account/api-keys., url: https://api.openai.com/v1/responses, cf-ray: a11b34cebba09505-LHR, request id: req_79cc489e2bac4c1ea0ecb796ab39ab94"
    }
  }
}

In the original Zed implementation, the text now in additionalDetails was in data.message.

Another difference from the Zed implementation: the top-level message previously matched the definition in the JSON-RPC spec exactly, and additional detail was in data.message. So the error would have looked like:

{
  "jsonrpc": "2.0",
  "id": 3,
  "error": {
    "code": -32603,
    "message": "Internal error",
    "data": {
      "message": "unexpected status 401 Unauthorized: Incorrect API key provided: fdsa. You can find your API key at https://platform.openai.com/account/api-keys., url: https://api.openai.com/v1/responses, cf-ray: a11b34cebba09505-LHR, request id: req_79cc489e2bac4c1ea0ecb796ab39ab94",
...

[anvilpete]

(the exact shape probably isn't too important, but it would be nice to avoid the "Reconnecting... 5/5")

[benbrandt]

great catch thanks, fixing