Add plan C: Javascript way

modules/custom/instagram_graphql/instagram_graphql.libraries.yml

+fetcher:
+  version: VERSION
+  js:
+    js/instagram.fetcher.js: {}
+  dependencies:
+    - core/jquery.once

modules/custom/instagram_graphql/js/instagram.fetcher.js

+(function ($) {
+  Drupal.behaviors.instagramFetcher = {
+    attach: function (context, settings) {
+      // Apply jQuery.once behavior.
+      $('.field--name-field-instagram-account', context)
+        .once('instagram-fetcher')
+        .each(function () {
+          // Verify instagram settings are available.
+          if (typeof drupalSettings.instagram === "object") {
+            // Consume Instagram account homepage by HTTP GET method.
+            var url = 'https://www.instagram.com/' + settings.instagram.account;
+            $.ajax({
+              type: 'GET',
+              url: url,
+              error: function (e) {
+                console.error(e);
+              },
+              success: function (response) {
+                var data = Drupal.behaviors.instagramFetcher.prepareResponse(response);
+                if (data !== null) {
+                  var cards = Drupal.behaviors.instagramFetcher.buildCards(data);
+                  console.log(cards);
+                }
+              }
+            });
+          }
+        });
+    },
+    prepareResponse: function (response) {
+      var data = null;
+      try {
+        var entry = JSON.parse(
+          response.split("window._sharedData = ")[1]
+            .split(";</script>")[0]
+        ).entry_data;
+
+        if(entry.ProfilePage) {
+          data = entry.ProfilePage[0].graphql;
+        }
+      } catch (e) {
+        console.error(e);
+      }
+
+      return data;
+    },
+    buildCards: function (data)  {
+      if (typeof data.user === 'object' &&
+        typeof data.user.edge_owner_to_timeline_media === 'object' &&
+        typeof data.user.edge_owner_to_timeline_media.edges === 'object') {
+
+        var cards = [];
+        var edges = data.user.edge_owner_to_timeline_media.edges;
+        for (var idx in edges) {
+          var edge = edges[idx].node;
+          cards.push({
+            'username': edge.owner.username,
+            'image_url': edge.display_url,
+            'image_caption': edge.accessibility_caption,
+            'description': edge.edge_media_to_caption.edges[0].node.text
+          });
+          if (cards.length >= 10) {
+            break;
+          }
+        }
+        return cards;
+      }
+
+    }
+  };
+})(jQuery);

modules/custom/instagram_graphql/src/Plugin/Field/FieldFormatter/InstagramGraphQLFormatter.php

@@ -33,6 +33,10 @@ public function viewElements(FieldItemListInterface $items, $langcode) {
           'sharedData' => $this->getSharedData($item->value),
         ],
       ];
+
+      // Plan C: By Javascript...
+      $element[$delta]['#attached']['drupalSettings']['instagram']['account'] = $item->value;
+      $element[$delta]['#attached']['library'][] = 'instagram_graphql/fetcher';
     }
 
     return $element;
@@ -84,7 +88,7 @@ protected function getSharedData($username) {
           'text',
         ]),
       ];
-    }, $rawData);
+    }, $rawData ?? []);
   }
 
 }