fix(coderd/x/chatd): show correct provider and clean detail for Bedrock errors (#26338)

## Problem
Bedrock errors (routed through aibridge) showed the wrong provider
("Anthropic ...")
and a doubly-wrapped detail string instead of the clean message.

## Fix (chatd only)
- **Provider label:** thread the configured provider to error
classification via
`GenerateAssistantOptions.ErrorProvider`. Transport provider still
drives prompt
  prep, sanitization, and metric labels (unchanged).
- **Detail:** unwrap the SDK transport wrapper (`METHOD "URL": NNN
{body}`) to surface
the inner message; handles top-level `{"message":...}` and nested
`{"error":{"message":...}}`.

## Notes
- Surfacing a top-level `message` now applies to all providers
(intentional; nested wins when both present).
- The advisor path keeps the transport label; accepted as-is (it returns
`err.Error()`, not the classification).
- Fixes display in chatd only; the wrapper originates in aibridge (out
of scope here).

🤖 Generated by Coder Agents.

coderd/x/chatd/chatloop/chatloop_run_internal_test.go

@@ -171,6 +171,33 @@ func TestGenerateAssistant_ProviderContextSurvivesStreamError(t *testing.T) {
 	require.Equal(t, "OpenAI returned an unexpected error.", classified.Message)
 }
 
+func TestGenerateAssistant_ErrorProviderOverridesTransportLabel(t *testing.T) {
+	t.Parallel()
+
+	// Bedrock routed through aibridge uses the Anthropic transport, so
+	// Model.Provider() reports "anthropic". The user-facing error must use
+	// the configured provider from ErrorProvider instead.
+	model := &chattest.FakeModel{
+		ProviderName: "anthropic",
+		ModelName:    "qwen3-coder-next",
+		StreamFn: func(_ context.Context, _ fantasy.Call) (fantasy.StreamResponse, error) {
+			return nil, xerrors.New("upstream returned status 400")
+		},
+	}
+
+	_, err := GenerateAssistant(context.Background(), GenerateAssistantOptions{
+		Model:         model,
+		ErrorProvider: "bedrock",
+		Messages: []fantasy.Message{
+			textMessage(fantasy.MessageRoleUser, "hello"),
+		},
+	})
+	require.Error(t, err)
+	classified := chaterror.Classify(err)
+	require.Equal(t, "bedrock", classified.Provider)
+	require.Equal(t, "AWS Bedrock returned an unexpected error.", classified.Message)
+}
+
 func TestGenerateAssistant_HTTP2TransportErrorClassifiedAsRetryableTimeout(t *testing.T) {
 	t.Parallel()