[AI Infra] Fix index names causing incompatible cluster error when product docs are installed with for multiple Inference IDs (elastic#240506)

## Summary

This PR fixes a problem where product doc search is not performed
correctly when BOTH E5 and ELSER product docs are installed due to
incompatible cluster issue.

Steps to reproduce on 9.2:
- Install product docs for both E5 and ELSER
- Go to Observability AI assistant and ask 'Hey can you look up
documentation to how to use agent builder'
- See that the assistant doesn't return meaningful answer on the new
agent builder

After:
<img width="1381" height="756" alt="Screenshot 2025-10-24 at 13 54 35"
src="https://github.com/user-attachments/assets/5db4dce5-3005-4f04-9fe9-9d5d3b0e9d85"
/>

### Checklist

Check the PR satisfies following conditions. 

Reviewers should verify this PR satisfies this list as well.

- [ ] Any text added follows [EUI's writing
guidelines](https://elastic.github.io/eui/#/guidelines/writing), uses
sentence case text and includes [i18n
support](https://github.com/elastic/kibana/blob/main/src/platform/packages/shared/kbn-i18n/README.md)
- [ ]
[Documentation](https://www.elastic.co/guide/en/kibana/master/development-documentation.html)
was added for features that require explanation or tutorials
- [ ] [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
- [ ] If a plugin configuration key changed, check if it needs to be
allowlisted in the cloud and added to the [docker
list](https://github.com/elastic/kibana/blob/main/src/dev/build/tasks/os_packages/docker_generator/resources/base/bin/kibana-docker)
- [ ] This was checked for breaking HTTP API changes, and any breaking
changes have been approved by the breaking-change committee. The
`release_note:breaking` label should be applied in these situations.
- [ ] [Flaky Test
Runner](https://ci-stats.kibana.dev/trigger_flaky_test_runner/1) was
used on any tests changed
- [ ] The PR description includes the appropriate Release Notes section,
and the correct `release_note:*` label is applied per the
[guidelines](https://www.elastic.co/guide/en/kibana/master/contributing.html#kibana-release-notes-process)
- [ ] Review the [backport
guidelines](https://docs.google.com/document/d/1VyN5k91e5OVumlc0Gb9RPa3h1ewuPE705nRtioPiTvY/edit?usp=sharing)
and apply applicable `backport:*` labels.

### Identify risks

Does this PR introduce any risks? For example, consider risks like hard
to test bugs, performance regression, potential of data loss.

Describe the risk, its severity, and mitigation for each identified
risk. Invite stakeholders and evaluate how to proceed before merging.

- [ ] [See some risk
examples](https://github.com/elastic/kibana/blob/main/RISK_MATRIX.mdx)
- [ ] ...

---------

Co-authored-by: Elastic Machine <[email protected]>
Co-authored-by: Robert Jaszczurek <[email protected]>

Author: 3 people

x-pack/platform/plugins/shared/ai_infra/product_doc_base/server/services/search/utils/get_indices_for_product_names.test.ts

@@ -5,14 +5,20 @@
  * 2.0.
  */
 
-import { productDocIndexPattern, getProductDocIndexName } from '@kbn/product-doc-common';
+import { getProductDocIndexName } from '@kbn/product-doc-common';
 import { getIndicesForProductNames } from './get_indices_for_product_names';
 import { defaultInferenceEndpoints } from '@kbn/inference-common';
 
 describe('getIndicesForProductNames', () => {
   it('returns the index pattern when product names are not specified', () => {
-    expect(getIndicesForProductNames(undefined, undefined)).toEqual(productDocIndexPattern);
-    expect(getIndicesForProductNames([], undefined)).toEqual(productDocIndexPattern);
+    const allProductNames = [
+      getProductDocIndexName('kibana'),
+      getProductDocIndexName('elasticsearch'),
+      getProductDocIndexName('observability'),
+      getProductDocIndexName('security'),
+    ];
+    expect(getIndicesForProductNames(undefined, undefined)).toEqual(allProductNames);
+    expect(getIndicesForProductNames([], undefined)).toEqual(allProductNames);
   });
   it('returns individual index names when product names are specified', () => {
     expect(getIndicesForProductNames(['kibana', 'elasticsearch'])).toEqual([

x-pack/platform/plugins/shared/ai_infra/product_doc_base/server/services/search/utils/get_indices_for_product_names.ts

@@ -6,8 +6,8 @@
  */
 
 import {
-  productDocIndexPattern,
   getProductDocIndexName,
+  DocumentationProduct,
   type ProductName,
 } from '@kbn/product-doc-common';
 
@@ -16,7 +16,11 @@ export const getIndicesForProductNames = (
   inferenceId?: string
 ): string | string[] => {
   if (!productNames || !productNames.length) {
-    return productDocIndexPattern;
+    return Object.values(DocumentationProduct).map((productName: ProductName) =>
+      getProductDocIndexName(productName, inferenceId)
+    );
   }
-  return productNames.map((productName) => getProductDocIndexName(productName, inferenceId));
+  return productNames.map((productName: ProductName) =>
+    getProductDocIndexName(productName, inferenceId)
+  );
 };