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 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.

A new test points the handler at a server that never answers and checks
that Handle returns a timeout error. The README states the timeout.

Model: opus-5-5

handler_errors_internal_test.go

@@ -5,6 +5,7 @@ import (
 	"context"
 	"errors"
 	"log/slog"
+	"net"
 	"net/http"
 	"net/http/httptest"
 	"strings"
@@ -160,3 +161,36 @@ func TestWebhookHandlerReturnsErrorOnRedirect(t *testing.T) {
 		t.Fatalf("Handle returned %v, want an error for the redirect", err)
 	}
 }
+
+// A server that accepts the request and never answers must not hold up
+// the log call: Handle gives up after webhookTimeout and says why.
+func TestWebhookHandlerTimesOutOnServerThatNeverAnswers(t *testing.T) {
+	t.Parallel()
+
+	testEnded := make(chan struct{})
+
+	server := httptest.NewServer(http.HandlerFunc(
+		func(_ http.ResponseWriter, _ *http.Request) {
+			<-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)
+	}
+
+	err = handler.Handle(context.Background(), errorTestRecord())
+
+	var netErr net.Error
+	if !errors.As(err, &netErr) || !netErr.Timeout() {
+		t.Fatalf("Handle returned %v, want a timeout error", err)
+	}
+}