Give the webhook handler a timeout (closes #38)

The webhook handler's client had no timeout, and slog calls the handler
inside the log call, so a server that accepted the connection and never
answered stopped that log call for good, and every later one. A request
still running after 5 seconds, reading the answer included, now fails
with a timeout error. The handler also reads the answer to the end
before closing it, so the connection is reused for the next record.

Two new tests point the handler at a server that never answers and at
one that sends its status and then stalls the answer, and check that
Handle returns a timeout error within the timeout. The README states
the timeout.

Model: opus-5-5

handler_errors_internal_test.go

@@ -187,7 +187,74 @@ func TestWebhookHandlerTimesOutOnServerThatNeverAnswers(t *testing.T) {
 		t.Fatalf("NewWebhookHandler: %v", err)
 	}
 
-	err = handler.Handle(context.Background(), errorTestRecord())
+	// Handle runs in a goroutine so that a lost timeout fails the test
+	// instead of hanging the test run.
+	handleErr := make(chan error, 1)
+
+	go func() {
+		handleErr <- handler.Handle(context.Background(), errorTestRecord())
+	}()
+
+	select {
+	case err = <-handleErr:
+	case <-time.After(webhookTimeout + time.Second):
+		t.Fatal("Handle did not return within webhookTimeout")
+	}
+
+	var netErr net.Error
+	if !errors.As(err, &netErr) || !netErr.Timeout() {
+		t.Fatalf("Handle returned %v, want a timeout error", err)
+	}
+}
+
+// A server that sends a 2xx status and then never finishes the answer
+// must not hold up the log call either: reading the answer counts toward
+// webhookTimeout, and Handle returns the read's error.
+func TestWebhookHandlerTimesOutOnServerThatStallsTheAnswer(t *testing.T) {
+	t.Parallel()
+
+	testEnded := make(chan struct{})
+
+	server := httptest.NewServer(http.HandlerFunc(
+		func(w http.ResponseWriter, _ *http.Request) {
+			w.WriteHeader(http.StatusOK)
+
+			// Flush sends the status now; the answer stays unfinished
+			// until the test ends.
+			err := http.NewResponseController(w).Flush()
+			if err != nil {
+				t.Errorf("flush the status: %v", err)
+			}
+
+			<-testEnded
+		},
+	))
+
+	// server.Close waits for running requests, so the server's handler
+	// is released first.
+	defer func() {
+		close(testEnded)
+		server.Close()
+	}()
+
+	handler, err := NewWebhookHandler(server.URL)
+	if err != nil {
+		t.Fatalf("NewWebhookHandler: %v", err)
+	}
+
+	// Handle runs in a goroutine so that a lost timeout fails the test
+	// instead of hanging the test run.
+	handleErr := make(chan error, 1)
+
+	go func() {
+		handleErr <- handler.Handle(context.Background(), errorTestRecord())
+	}()
+
+	select {
+	case err = <-handleErr:
+	case <-time.After(webhookTimeout + time.Second):
+		t.Fatal("Handle did not return within webhookTimeout")
+	}
 
 	var netErr net.Error
 	if !errors.As(err, &netErr) || !netErr.Timeout() {

webhook_handler.go

@@ -113,12 +113,16 @@ func (w *WebhookHandler) Handle(ctx context.Context, record slog.Record) error {
 		return err
 	}
 
-	// The answer is read to the end before closing, so the client can
-	// reuse the connection for the next record.
-	defer func() {
-		_, _ = io.Copy(io.Discard, response.Body)
-		_ = response.Body.Close()
-	}()
+	defer func() { _ = response.Body.Close() }()
+
+	// The answer is read to the end so the client can reuse the
+	// connection for the next record. The read counts toward
+	// webhookTimeout, so a server that sends its status and then stalls
+	// fails here.
+	_, err = io.Copy(io.Discard, response.Body)
+	if err != nil {
+		return err
+	}
 
 	if response.StatusCode < http.StatusOK ||
 		response.StatusCode >= http.StatusMultipleChoices {