fix(auth): preserve User-Agent in authflow getViewer

getViewer was building a new HTTP client from scratch, losing
AppVersion and InvokingAgent from the plain client already passed
into AuthFlow. Reuse the existing client by shallow-copying it and
wrapping its transport with AddAuthTokenHeader for the new token.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

internal/authflow/flow.go

@@ -97,7 +97,7 @@ func AuthFlow(httpClient *http.Client, oauthHost string, IO *iostreams.IOStreams
 		return "", "", err
 	}
 
-	userLogin, err := getViewer(oauthHost, token.Token, IO.ErrOut)
+	userLogin, err := getViewer(httpClient, oauthHost, token.Token)
 	if err != nil {
 		return "", "", err
 	}
@@ -123,16 +123,10 @@ func (c cfg) ActiveToken(hostname string) (string, string) {
 	return c.token, "oauth_token"
 }
 
-func getViewer(hostname, token string, logWriter io.Writer) (string, error) {
-	opts := api.HTTPClientOptions{
-		Config: cfg{token: token},
-		Log:    logWriter,
-	}
-	client, err := api.NewHTTPClient(opts)
-	if err != nil {
-		return "", err
-	}
-	return api.CurrentLoginName(api.NewClientFromHTTP(client), hostname)
+func getViewer(httpClient *http.Client, hostname, token string) (string, error) {
+	authedClient := *httpClient
+	authedClient.Transport = api.AddAuthTokenHeader(httpClient.Transport, cfg{token: token})
+	return api.CurrentLoginName(api.NewClientFromHTTP(&authedClient), hostname)
 }
 
 func waitForEnter(r io.Reader) error {

internal/authflow/flow_test.go

@@ -1,11 +1,54 @@
 package authflow
 
 import (
+	"bytes"
+	"io"
+	"net/http"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
+func Test_getViewer_preservesUserAgent(t *testing.T) {
+	var receivedUA string
+	var receivedAuth string
+
+	// Outer transport sets User-Agent, simulating the factory-built client's header middleware.
+	// Inner transport captures headers as-received to verify they survived the wrapping.
+	plainClient := &http.Client{
+		Transport: &roundTripper{roundTrip: func(req *http.Request) (*http.Response, error) {
+			req.Header.Set("User-Agent", "GitHub CLI 1.2.3 Agent/copilot-cli")
+			return (&http.Client{
+				Transport: &roundTripper{roundTrip: func(req *http.Request) (*http.Response, error) {
+					receivedUA = req.Header.Get("User-Agent")
+					receivedAuth = req.Header.Get("Authorization")
+					return &http.Response{
+						StatusCode: 200,
+						Header:     http.Header{"Content-Type": []string{"application/json"}},
+						Body:       io.NopCloser(bytes.NewBufferString(`{"data":{"viewer":{"login":"monalisa"}}}`)),
+						Request:    req,
+					}, nil
+				}},
+			}).Transport.RoundTrip(req)
+		}},
+	}
+
+	login, err := getViewer(plainClient, "github.com", "test-token")
+	require.NoError(t, err)
+	assert.Equal(t, "monalisa", login)
+	assert.Equal(t, "GitHub CLI 1.2.3 Agent/copilot-cli", receivedUA)
+	assert.Equal(t, "token test-token", receivedAuth)
+}
+
+type roundTripper struct {
+	roundTrip func(*http.Request) (*http.Response, error)
+}
+
+func (t *roundTripper) RoundTrip(req *http.Request) (*http.Response, error) {
+	return t.roundTrip(req)
+}
+
 func Test_getCallbackURI(t *testing.T) {
 	tests := []struct {
 		name      string