[Streams] Add root stream processing CTA to partitioning (elastic#240964)

## 📓 Summary

Closes elastic#231318 

Quick change to add a CTA to bring users landing on a root stream
processing tab into the partitioning page.

<img width="3000" height="1583" alt="Screenshot 2025-10-28 at 11 53 54"
src="https://github.com/user-attachments/assets/51dd1dcd-661b-499c-9f50-4d54f025329e"
/>

Author: tonyghiani

x-pack/platform/plugins/shared/streams_app/public/components/data_management/stream_detail_enrichment/empty_prompts.tsx

@@ -6,12 +6,26 @@
  */
 
 import React from 'react';
-import { EuiEmptyPrompt, EuiFlexGroup, EuiFlexItem, EuiSpacer, EuiText } from '@elastic/eui';
+import {
+  EuiButton,
+  EuiEmptyPrompt,
+  EuiFlexGroup,
+  EuiFlexItem,
+  EuiSpacer,
+  EuiText,
+} from '@elastic/eui';
 import { i18n } from '@kbn/i18n';
+import { useStreamsAppParams } from '../../../hooks/use_streams_app_params';
+import { useStreamsAppRouter } from '../../../hooks/use_streams_app_router';
 import { AssetImage } from '../../asset_image';
 import { CreateStepButton } from './create_step_button';
 
 export const RootStreamEmptyPrompt = () => {
+  const router = useStreamsAppRouter();
+  const {
+    path: { key: streamName },
+  } = useStreamsAppParams('/{key}/management/{tab}');
+
   return (
     <EuiEmptyPrompt
       aria-live="polite"
@@ -36,6 +50,23 @@ export const RootStreamEmptyPrompt = () => {
           )}
         </p>
       }
+      actions={
+        <EuiButton
+          href={router.link('/{key}/management/{tab}', {
+            path: {
+              key: streamName,
+              tab: 'partitioning',
+            },
+          })}
+        >
+          {i18n.translate(
+            'xpack.streams.streamDetailView.managementTab.rootStreamEmptyPrompt.button',
+            {
+              defaultMessage: 'Open stream partitioning',
+            }
+          )}
+        </EuiButton>
+      }
     />
   );
 };