or maybe like that?

apps/monitoring/thanos.statefulset.yaml

@@ -22,7 +22,7 @@ spec:
           args:
           - "store"
           - "--log.level=debug"
-          # - "--data-dir=/data"
+          - "--data-dir=/data"
           - "--objstore.config-file=/etc/secret/thanos.yaml"
           - "--index-cache-size=500MB"
           - "--chunk-pool-size=500MB"
@@ -43,7 +43,11 @@ spec:
             - name: thanos-objstore-config
               mountPath: /etc/secret
               readOnly: true
+            - name: thanos-data
+              mountPath: /data
       volumes:
         - name: thanos-objstore-config
           secret:
             secretName: thanos-objstore-config
+        - name: thanos-data
+          emptyDir: {}