[Response Ops] Fix Task Manager Remove Types Flaky Test (#201728)

## Summary

Issue: #200154

Fixes flaky task manager remove types test by following the guidance
here: #161882

### Checklist
- [x] [Unit or functional
tests](https://www.elastic.co/guide/en/kibana/master/development-tests.html)
were updated or added to match the most common scenarios

x-pack/test/functional/es_archives/task_manager_removed_types/data.json

@@ -2,11 +2,9 @@
   "type": "doc",
   "value": {
     "id": "task:ce7e1250-3322-11eb-94c1-db6995e83f6b",
-    "index": ".kibana_task_manager_1",
+    "index": ".kibana_task_manager",
     "source": {
-      "migrationVersion": {
-        "task": "7.6.0"
-      },
+      "typeMigrationVersion": "7.6.0",
       "references": [
       ],
       "task": {
@@ -33,11 +31,9 @@
   "type": "doc",
   "value": {
     "id": "task:be7e1250-3322-11eb-94c1-db6995e83f6a",
-    "index": ".kibana_task_manager_1",
+    "index": ".kibana_task_manager",
     "source": {
-      "migrationVersion": {
-        "task": "7.6.0"
-      },
+      "typeMigrationVersion": "7.6.0",
       "references": [
       ],
       "task": {

x-pack/test/plugin_api_integration/test_suites/task_manager/task_management_removed_types.ts

@@ -47,8 +47,7 @@ export default function ({ getService }: FtrProviderContext) {
   const UNREGISTERED_TASK_TYPE_ID = 'ce7e1250-3322-11eb-94c1-db6995e83f6b';
   const REMOVED_TASK_TYPE_ID = 'be7e1250-3322-11eb-94c1-db6995e83f6a';
 
-  // FLAKY: https://github.com/elastic/kibana/issues/200154
-  describe.skip('not registered task types', () => {
+  describe('not registered task types', () => {
     before(async () => {
       await esArchiver.load('x-pack/test/functional/es_archives/task_manager_removed_types');
     });