[DOC] Document search API (#5521)

## 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](https://github.com/chroma-core/chroma/tree/main/docs/docs.trychroma.com)?_

---------

Co-authored-by: Philip I. Thomas <[email protected]>

Author: Sicheng-Pan

docs/docs.trychroma.com/markdoc/content/cloud/getting-started.md

@@ -25,4 +25,8 @@ Chroma Cloud is SOC 2 Type I certified (Type II in progress), and offers deploym
 
 Our web dashboard lets your team work together to view your data, and ensure data quality in your collections with ease. It also serves as a touchpoint for you to view billing data and usage telemetry.
 
+### Advanced Search API (Beta)
+
+Chroma Cloud introduces a powerful [Search API](/cloud/search-api/overview) that enables hybrid search with advanced filtering, custom ranking expressions, and batch operations. Combine vector similarity with metadata filtering using an intuitive builder pattern or flexible dictionary syntax.
+
 Chroma Cloud is open-source at its core, built on the exact same Apache 2.0 codebase available to everyone. Whether you’re building a prototype or running a mission-critical production workload, Chroma Cloud is the fastest path to reliable, scalable, and accurate retrieval.