master: update href links of developer guides and vector search docs in _docHome.md

[qiancai]

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[gemini-code-assist]

Summary of Changes

Hello @qiancai, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request refines the navigation experience on the documentation homepage by updating several DocHomeCard links and labels. The changes standardize the paths for developer guides and improve the clarity of the vector search documentation entry, ensuring users are directed to the correct and most relevant content with consistent labeling.

Highlights

• Developer Guide Links: Updated the href attribute for both TiDB Cloud and TiDB Self-Managed 'Developer Guide' DocHomeCards to a standardized /developer/ path, ensuring consistent navigation.
• Vector Search Link and Label: Modified the href for the 'Vector Search' DocHomeCard from /tidbcloud/vector-search-overview to /ai/vector-search-overview and simplified its label from 'Vector Search in TiDB Cloud (Beta)' to 'Vector Search (Beta)'.
• Developer Guide Description: Revised the descriptive text for the TiDB Self-Managed 'Developer Guide' DocHomeCard to 'Connect your application with the languages and frameworks you prefer.', aligning it with the TiDB Cloud version.

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Changelog

• _docHome.md
  • Updated 'Developer Guide' href from '/tidbcloud/dev-guide-overview' to '/developer/'.
  • Updated 'Vector Search in TiDB Cloud (Beta)' href from '/tidbcloud/vector-search-overview' to '/ai/vector-search-overview'.
  • Updated 'Vector Search in TiDB Cloud (Beta)' label to 'Vector Search (Beta)'.
  • Updated 'Developer Guide' href from '/tidb/stable/dev-guide-overview' to '/developer/'.
  • Updated 'Developer Guide' body text from 'For application developers using TiDB Self-Managed.' to 'Connect your application with the languages and frameworks you prefer.'.

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[gemini-code-assist]

Code Review

This pull request effectively refactors the main documentation homepage by updating several key links and descriptions. The developer guides for both TiDB Cloud and Self-Managed now correctly point to the unified /developer/ page, and the vector search documentation link is also updated. The accompanying text changes, such as simplifying the 'Vector Search' label and improving the 'Developer Guide' description for consistency, enhance clarity and readability. Overall, these are positive changes that improve the structure and user-friendliness of the documentation.

[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-02-12 10:07:11.618861093 +0000 UTC m=+99384.698851788: ☑️ agreed by Oreoxmt.

[qiancai]

/approve

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: qiancai

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[ti-chi-bot]

In response to a cherrypick label: new pull request created to branch release-8.5: #22452.
But this PR has conflicts, please resolve them!