diff --git a/CHANGELOG.md b/CHANGELOG.md
index 577678ef..2584a815 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -38,6 +38,10 @@ All notable changes to this project will be documented in this file.
   discarded when the application references a SparkApplicationTemplate. The overrides of the
   template are now applied first and the ones of the SparkApplication on top of them, so an
   application can also remove a JVM argument that one of its templates added ([#745]).
+- BREAKING: The connect and history-server listener PVC templates now carry the recommended
+  labels without the version label, so that the labels stay stable across upgrades.
+  Existing connect and history-server StatefulSets must be deleted once before the new operator
+  can reconcile them (connect server: [#750], history server: [#753]).
 
 [#721]: https://github.com/stackabletech/spark-k8s-operator/pull/721
 [#727]: https://github.com/stackabletech/spark-k8s-operator/pull/727
@@ -45,6 +49,7 @@ All notable changes to this project will be documented in this file.
 [#744]: https://github.com/stackabletech/spark-k8s-operator/pull/744
 [#745]: https://github.com/stackabletech/spark-k8s-operator/pull/745
 [#746]: https://github.com/stackabletech/spark-k8s-operator/pull/746
+[#750]: https://github.com/stackabletech/spark-k8s-operator/pull/750
 [#753]: https://github.com/stackabletech/spark-k8s-operator/pull/753
 
 ## [26.7.0] - 2026-07-21
diff --git a/rust/operator-binary/src/connect/controller/build/mod.rs b/rust/operator-binary/src/connect/controller/build/mod.rs
index 5dffa384..2a43fc9a 100644
--- a/rust/operator-binary/src/connect/controller/build/mod.rs
+++ b/rust/operator-binary/src/connect/controller/build/mod.rs
@@ -166,6 +166,25 @@ pub(crate) fn recommended_labels_for_role_resources(
     )
 }
 
+/// Recommended labels for role resources which cannot be mutated and should therefore not
+/// include the product version, like the listener PVC in the StatefulSet's
+/// `volumeClaimTemplates`.
+///
+/// Spark Connect has no role groups, so all role resources use these labels (without a role
+/// group label).
+pub(crate) fn recommended_labels_for_unversioned_role_resources(
+    server: &ValidatedSparkConnectServer,
+    role_name: &RoleName,
+) -> Labels {
+    Labels::from_iter([
+        label::label_app_kubernetes_io_instance(&server.name),
+        label::label_app_kubernetes_io_name(&PRODUCT_NAME),
+        label::label_app_kubernetes_io_component(role_name),
+        label::label_app_kubernetes_io_managed_by(&OPERATOR_NAME, &CONTROLLER_NAME),
+        label::label_stackable_tech_vendor(),
+    ])
+}
+
 /// Selector labels matching the pods of the given role.
 pub(crate) fn role_selector(server: &ValidatedSparkConnectServer, role_name: &RoleName) -> Labels {
     label::role_selector(&server.name, &PRODUCT_NAME, role_name)
diff --git a/rust/operator-binary/src/connect/controller/build/server.rs b/rust/operator-binary/src/connect/controller/build/server.rs
index 419bfefc..007d3307 100644
--- a/rust/operator-binary/src/connect/controller/build/server.rs
+++ b/rust/operator-binary/src/connect/controller/build/server.rs
@@ -44,7 +44,10 @@ use crate::{
         GRPC, HTTP,
         common::{self, SparkConnectRole, object_name},
         controller::{
-            build::{object_meta, recommended_labels_for_role_resources, role_selector},
+            build::{
+                object_meta, recommended_labels_for_role_resources,
+                recommended_labels_for_unversioned_role_resources, role_selector,
+            },
             validate::ValidatedSparkConnectServer,
         },
         crd::{
@@ -289,6 +292,11 @@ pub(crate) fn build_stateful_set(
         ));
     }
 
+    // Used for the listener PVC template, which cannot be modified once it is deployed. The
+    // version label is omitted so the labels stay stable across version upgrades.
+    let unversioned_recommended_labels =
+        recommended_labels_for_unversioned_role_resources(validated, &SparkConnectRole::Server);
+
     // Add listener volume
     // Listener endpoints for the Webserver role will use persistent volumes
     // so that load balancers can hard-code the target addresses. This will
@@ -297,7 +305,7 @@ pub(crate) fn build_stateful_set(
     let volume_claim_templates = Some(vec![
         ListenerOperatorVolumeSourceBuilder::new(
             &ListenerReference::ListenerName(listener_name.to_string()),
-            &recommended_labels,
+            &unversioned_recommended_labels,
         )
         .build_pvc(LISTENER_VOLUME_NAME.to_string())
         .context(BuildListenerVolumeSnafu)?,
diff --git a/tests/templates/kuttl/smoke/50-assert.yaml b/tests/templates/kuttl/smoke/50-assert.yaml
index 1319f33a..a6f2e4ca 100644
--- a/tests/templates/kuttl/smoke/50-assert.yaml
+++ b/tests/templates/kuttl/smoke/50-assert.yaml
@@ -11,5 +11,11 @@ apiVersion: kuttl.dev/v1beta1
 kind: TestAssert
 commands:
   - script: |
+      # Wait for the spark-submit pod: the image pull can take minutes and
+      # kuttl would otherwise retry (and log) this whole script every second.
+      kubectl wait -n $NAMESPACE pod \
+          --selector batch.kubernetes.io/job-name=spark-pi-s3-1 \
+          --for=jsonpath='{.status.phase}'=Running \
+          --timeout=280s > /dev/null 2>&1 || exit 1
       SPARK_SUBMIT_POD=$(kubectl get -n $NAMESPACE pods --field-selector=status.phase=Running --selector batch.kubernetes.io/job-name=spark-pi-s3-1 -o jsonpath='{.items[0].metadata.name}')
       kubectl exec -n $NAMESPACE --container spark-submit $SPARK_SUBMIT_POD -- cat /stackable/log/containerdebug-state.json | jq --exit-status '"valid JSON"'