Bind path navigation to stage data

ee/app/assets/javascripts/analytics/cycle_analytics/components/base.vue

@@ -194,6 +194,7 @@ export default {
       <div class="gl-mt-3 gl-py-2 gl-px-3 bg-gray-light border-top border-bottom">
         <div v-if="shouldDisplayPathNavigation" class="gl-w-full gl-pb-2">
           <path-navigation
+            :key="`path_navigation_key_${pathNavigationData.length}`"
             class="js-path-navigation"
             :loading="isLoading"
             :stages="pathNavigationData"

ee/changelogs/unreleased/283983-vsa-path-navigation-carousel-not-dynamically-updating.yml

+---
+title: Refresh VSA path navigation carousel when updating stage data
+merge_request: 51187
+author:
+type: fixed