Propagate label selector click when embedded

app/assets/javascripts/vue_shared/components/sidebar/labels_select_vue/dropdown_button.vue

 <script>
-import { mapActions, mapGetters } from 'vuex';
+import { mapActions, mapGetters, mapState } from 'vuex';
 import { GlButton, GlIcon } from '@gitlab/ui';
 
 export default {
@@ -8,6 +8,7 @@ export default {
     GlIcon,
   },
   computed: {
+    ...mapState(['showDropdownContents']),
     ...mapGetters([
       'dropdownButtonText',
       'isDropdownVariantStandalone',
@@ -19,6 +20,9 @@ export default {
     handleButtonClick(e) {
       if (this.isDropdownVariantStandalone || this.isDropdownVariantEmbedded) {
         this.toggleDropdownContents();
+      }
+
+      if (this.isDropdownVariantStandalone) {
         e.stopPropagation();
       }
     },
@@ -31,9 +35,9 @@ export default {
     class="labels-select-dropdown-button js-dropdown-button w-100 text-left"
     @click="handleButtonClick"
   >
-    <span class="dropdown-toggle-text flex-fill">
+    <span class="dropdown-toggle-text gl-pointer-events-none flex-fill">
       {{ dropdownButtonText }}
     </span>
-    <gl-icon name="chevron-down" class="float-right" />
+    <gl-icon name="chevron-down" class="gl-pointer-events-none float-right" />
   </gl-button>
 </template>

spec/frontend/vue_shared/components/sidebar/labels_select_vue/dropdown_button_spec.js

@@ -45,7 +45,7 @@ describe('DropdownButton', () => {
         ${'standalone'}
         ${'embedded'}
       `(
-        'toggles dropdown content and stops event propagation when `state.variant` is "$variant"',
+        'toggles dropdown content and handles event propagation when `state.variant` is "$variant"',
         ({ variant }) => {
           const event = { stopPropagation: jest.fn() };
 
@@ -57,7 +57,12 @@ describe('DropdownButton', () => {
           findDropdownButton().vm.$emit('click', event);
 
           expect(store.state.showDropdownContents).toBe(true);
+
+          if (variant === 'standalone') {
             expect(event.stopPropagation).toHaveBeenCalled();
+          } else {
+            expect(event.stopPropagation).not.toHaveBeenCalled();
+          }
         },
       );
     });