Replace writeData with writeQuery Static Site Ed

app/assets/javascripts/static_site_editor/graphql/index.js

 import Vue from 'vue';
 import VueApollo from 'vue-apollo';
 import createDefaultClient from '~/lib/graphql';
+import appDataQuery from './queries/app_data.query.graphql';
 import fileResolver from './resolvers/file';
 import hasSubmittedChangesResolver from './resolvers/has_submitted_changes';
 import submitContentChangesResolver from './resolvers/submit_content_changes';
@@ -28,7 +29,8 @@ const createApolloProvider = (appData) => {
   // eslint-disable-next-line @gitlab/require-i18n-strings
   const mounts = appData.mounts.map((mount) => ({ __typename: 'Mount', ...mount }));
 
-  defaultClient.cache.writeData({
+  defaultClient.cache.writeQuery({
+    query: appDataQuery,
     data: {
       appData: {
         __typename: 'AppData',