[DOC] Document search API

[Sicheng-Pan]

Description of changes

Summarize the changes made by this PR.

• Improvements & Bug fixes
  • N/A
• New functionality
  • Adds search api documentation under chroma cloud section

Test plan

How are these changes tested?

• Tests pass locally with pytest for python, yarn test for js, cargo test for rust

Migration plan

Are there any migrations, or any forwards/backwards compatibility changes needed in order to make sure this change deploys reliably?

Observability plan

What is the plan to instrument and monitor this change?

Documentation Changes

Are all docstrings for user-facing APIs updated if required? Do we need to make documentation changes in the _docs section?_

[github-actions]

Reviewer Checklist

Please leverage this checklist to ensure your code review is thorough before approving

Testing, Bugs, Errors, Logs, Documentation

• Can you think of any use case in which the code does not behave as intended? Have they been tested?
• Can you think of any inputs or external events that could break the code? Is user input validated and safe? Have they been tested?
• If appropriate, are there adequate property based tests?
• If appropriate, are there adequate unit tests?
• Should any logging, debugging, tracing information be added or removed?
• Are error messages user-friendly?
• Have all documentation changes needed been made?
• Have all non-obvious changes been commented?

System Compatibility

• Are there any potential impacts on other parts of the system or backward compatibility?
• Does this change intersect with any items on our roadmap, and if so, is there a plan for fitting them together?

Quality

• Is this code of a unexpectedly high quality (Readability, Modularity, Intuitiveness)

[propel-code-bot]

Add Comprehensive Documentation for Chroma Cloud Search API

This PR introduces a new, detailed documentation suite for the Chroma Cloud Search API. It adds extensive multi-page docs, including an overview, quick start, API basics, filtering, ranking and scoring (with dictionary and builder syntax), hybrid search with RRF, pagination, batch operations, migration from legacy APIs, and end-to-end examples. The PR also updates the documentation sidebar navigation and references to surface the new Search API docs and links from Chroma Cloud onboarding materials.

Key Changes

• Added new documentation files under docs/docs.trychroma.com/markdoc/content/cloud/search-api/ covering: overview, search basics, filtering, ranking and scoring, hybrid search (RRF), examples, batch operations, migration, and pagination/field selection.
• Updated sidebar-config.ts to register a new 'Search API (Beta)' doc section under Chroma Cloud, listing all new Search API doc pages.
• Referenced Search API from the Chroma Cloud getting started docs and added informational notes to legacy Query and Get documentation to guide users to the Search API.
• Provides detailed, example-driven explanations (in both Python and TypeScript) of Search API usage: builder vs. dictionary syntax, K/Knn/Rrf usage, ranking operations, filtering logic, batch and hybrid search patterns, performance considerations, migration tips, and practical recipes.

Affected Areas

• docs/docs.trychroma.com/markdoc/content/cloud/search-api/ (all new)
• docs/docs.trychroma.com/markdoc/content/sidebar-config.ts
• docs/docs.trychroma.com/markdoc/content/cloud/getting-started.md
• docs/docs.trychroma.com/markdoc/content/docs/querying-collections/query-and-get.md

This summary was automatically generated by @propel-code-bot