Adds a new vector and full-text search quickstart

[kosabogi]

This PR adds a new vector and full-text search quickstart that:

• Guides users through connecting official Elasticsearch clients, creating an index, and indexing sample data.
• Demonstrates semantic search, hybrid search, and ES|QL aggregation.
• Provides examples and complete runnable scripts for Python, TypeScript, PHP, Ruby, C#/.NET, Java, and Go.

Testing

All seven client examples were tested end to end with Claude against Elasticsearch. The tests verified the expected search rankings and ES|QL aggregation output.

Generative AI disclosure

1. Did you use a generative AI (GenAI) tool to assist in creating this contribution?

• Yes
• No

Claude, Cursor - GPT 5.6

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🔍 Preview links for changed docs

• solutions/vector-database/vector-full-text-search.md

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[kosabogi]

Hi @alexmarhaba @dustincoates @georgewallace @KOTungseth @leemthompo ,

I've added the tutorial here, so please feel free to review it from now on.

These commits include the modifications we agreed on in our last call.

All commits include additional content refinements. I ran our review guidelines against this content and found a few areas that I thought would benefit from some small tweaks based on our guidelines. These include:

• Improved the introduction to clarify the tutorial’s purpose, audience, and expected outcomes
• Simplified the tutorial structure by removing unnecessary H3 headings
• Expanded a few explanations
• Replaced hardcoded product names with substitutions
• Organized the Next steps part into subsections
• Updated code examples based on end-to-end tests performed with Claude. For these, I'd love someone from the engineering team to take a close look even though the end-to-end tests were successful

All these changes are negotiable. Please let me know what you think.

Thank you in advance!

[leemthompo]

We need to tell folks how to find this: https://www.elastic.co/docs/solutions/elasticsearch-solution-project/search-connection-details

(#7709 is updating that page)

[dustincoates]

I took a quick glance and it looks good to me, thanks!

[yetanothertw]

If this page is intended for this particular project type, then we can use the new product id I've created for it.

See more details in https://github.com/elastic/docs-content-internal/issues/1534