[8.17] Update Search UI link targets (#204131) (#206627)

# Backport

This will backport the following commits from `main` to `8.17`:
- [Update Search UI link targets
(#204131)](https://github.com/elastic/kibana/pull/204131)

<!--- Backport version: 9.4.3 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sqren/backport)

<!--BACKPORT [{"author":{"name":"Colleen
McGinnis","email":"colleen.mcginnis@elastic.co"},"sourceCommit":{"committedDate":"2025-01-14T16:09:02Z","message":"Update
Search UI link targets (#204131)\n\n## Summary\r\n\r\nThis PR updates
the Kibana doc link service to target the new location\r\nof the Search
UI
docs\r\n(https://www.elastic.co/guide/en/search-ui/current/overview.html).
I\r\nwasn't totally sure which labels to apply but I pulled inspiration
from\r\na similar recent PR by
@lcawl\r\n(https://github.com/elastic/kibana/pull/199396).\r\n\r\n---------\r\n\r\nCo-authored-by:
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Search UI link
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Search UI link targets (#204131)\n\n## Summary\r\n\r\nThis PR updates
the Kibana doc link service to target the new location\r\nof the Search
UI
docs\r\n(https://www.elastic.co/guide/en/search-ui/current/overview.html).
I\r\nwasn't totally sure which labels to apply but I pulled inspiration
from\r\na similar recent PR by
@lcawl\r\n(https://github.com/elastic/kibana/pull/199396).\r\n\r\n---------\r\n\r\nCo-authored-by:
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Search UI link targets (#204131)\n\n## Summary\r\n\r\nThis PR updates
the Kibana doc link service to target the new location\r\nof the Search
UI
docs\r\n(https://www.elastic.co/guide/en/search-ui/current/overview.html).
I\r\nwasn't totally sure which labels to apply but I pulled inspiration
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BACKPORT-->

Co-authored-by: Colleen McGinnis <colleen.mcginnis@elastic.co>

packages/kbn-doc-links/src/get_doc_links.ts

@@ -22,7 +22,6 @@ export const getDocLinks = ({ kibanaBranch, buildFlavor }: GetDocLinkOptions): D
   const DOC_LINK_VERSION = meta.version;
   const ECS_VERSION = meta.ecs_version;
   const ELASTIC_WEBSITE_URL = meta.elasticWebsiteUrl;
-  const DOCS_WEBSITE_URL = meta.docsWebsiteUrl;
   const ELASTIC_GITHUB = meta.elasticGithubUrl;
   const SEARCH_LABS_URL = meta.searchLabsUrl;
 
@@ -38,7 +37,7 @@ export const getDocLinks = ({ kibanaBranch, buildFlavor }: GetDocLinkOptions): D
   const ENTERPRISE_SEARCH_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/enterprise-search/${DOC_LINK_VERSION}/`;
   const ESRE_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/esre/${DOC_LINK_VERSION}/`;
   const WORKPLACE_SEARCH_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/workplace-search/${DOC_LINK_VERSION}/`;
-  const SEARCH_UI_DOCS = `${DOCS_WEBSITE_URL}search-ui/`;
+  const SEARCH_UI_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/search-ui/current/`;
   const MACHINE_LEARNING_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/machine-learning/${DOC_LINK_VERSION}/`;
   const SERVERLESS_DOCS = `${ELASTIC_WEBSITE_URL}guide/en/serverless/current/`;
   const SEARCH_LABS_REPO = `${ELASTIC_GITHUB}elasticsearch-labs/`;