diff --git a/hack/update-codegen.sh b/hack/update-codegen.sh
index de795134..517986bb 100755
--- a/hack/update-codegen.sh
+++ b/hack/update-codegen.sh
@@ -8,47 +8,20 @@ set -o errexit
 set -o nounset
 set -o pipefail
 
+PROJECT_ROOT="$(dirname $0)"/..
+
 # setup virtual GOPATH
 source "$GARDENER_HACK_DIR"/vgopath-setup.sh
 
 CODE_GEN_DIR=$(go list -m -f '{{.Dir}}' k8s.io/code-generator)
-
-# We need to explicitly pass GO111MODULE=off to k8s.io/code-generator as it is significantly slower otherwise,
-# see https://github.com/kubernetes/code-generator/issues/100.
-export GO111MODULE=off
+source "${CODE_GEN_DIR}/kube_codegen.sh"
 
 rm -f $GOPATH/bin/*-gen
 
-bash "${CODE_GEN_DIR}"/generate-internal-groups.sh \
-  deepcopy,defaulter \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/client \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg \
-  "apis:v1alpha1" \
-  --go-header-file "${GARDENER_HACK_DIR}/LICENSE_BOILERPLATE.txt"
-
-bash "${CODE_GEN_DIR}"/generate-internal-groups.sh \
-  conversion \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/client \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg \
-  "apis:v1alpha1" \
-  --extra-peer-dirs=github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis/v1alpha1,github.com/gardener/external-dns-management/pkg/apis/dns/v1alpha1,k8s.io/apimachinery/pkg/apis/meta/v1,k8s.io/apimachinery/pkg/conversion,k8s.io/apimachinery/pkg/runtime \
-  --go-header-file "${GARDENER_HACK_DIR}/LICENSE_BOILERPLATE.txt"
-
-bash "${CODE_GEN_DIR}"/generate-internal-groups.sh \
-  deepcopy,defaulter \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/client \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis \
-  "service:v1alpha1" \
-  --go-header-file "${GARDENER_HACK_DIR}/LICENSE_BOILERPLATE.txt"
-
-bash "${CODE_GEN_DIR}"/generate-internal-groups.sh \
-  conversion \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/client \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis \
-  github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis \
-  "service:v1alpha1" \
-  --extra-peer-dirs=github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis/service,github.com/gardener/gardener-extension-shoot-dns-service/pkg/apis/service/v1alpha1,k8s.io/apimachinery/pkg/apis/meta/v1,k8s.io/apimachinery/pkg/conversion,k8s.io/apimachinery/pkg/runtime \
-  --go-header-file "${GARDENER_HACK_DIR}/LICENSE_BOILERPLATE.txt"
+kube::codegen::gen_helpers \
+  --boilerplate "${GARDENER_HACK_DIR}/LICENSE_BOILERPLATE.txt" \
+    --extra-peer-dir k8s.io/apimachinery/pkg/apis/meta/v1 \
+    --extra-peer-dir k8s.io/apimachinery/pkg/conversion \
+    --extra-peer-dir k8s.io/component-base/config \
+    --extra-peer-dir k8s.io/component-base/config/v1alpha1 \
+  "${PROJECT_ROOT}/pkg/apis"
diff --git a/pkg/controller/replication/add.go b/pkg/controller/replication/add.go
index da77dc6f..49f38f1c 100644
--- a/pkg/controller/replication/add.go
+++ b/pkg/controller/replication/add.go
@@ -63,5 +63,12 @@ func AddToManager(ctx context.Context, mgr manager.Manager) error {
 		return err
 	}
 	predicate := ForService(common.ShootDNSEntryLabelKey)
-	return ctrl.Watch(source.Kind(mgr.GetCache(), &dnsapi.DNSEntry{}), &handler.EnqueueRequestForObject{}, predicate)
+	return ctrl.Watch(
+		source.Kind[client.Object](
+			mgr.GetCache(),
+			&dnsapi.DNSEntry{},
+			&handler.EnqueueRequestForObject{},
+			predicate,
+		),
+	)
 }