docs: api separation (#3630)

# What does this PR do?

First step towards cleaning up the API reference section of the docs.

- Separates API reference into 3 sections: stable (`v1`), experimental (`v1alpha` and `v1beta`), and deprecated (`deprecated=True`)
- Each section is accessible via the dropdown menu and `docs/api-overview`

<img width="1237" height="321" alt="Screenshot 2025-09-30 at 5 47 30 PM" src="https://github.com/user-attachments/assets/fe0e498c-b066-46ed-a48e-4739d3b6724c" />

<img width="860" height="510" alt="Screenshot 2025-09-30 at 5 47 49 PM" src="https://github.com/user-attachments/assets/a92a8d8c-94bf-42d5-9f5b-b47bb2b14f9c" />

- Deprecated APIs: Added styling to the sidebar, and a notice on the endpoint pages

<img width="867" height="428" alt="Screenshot 2025-09-30 at 5 47 43 PM" src="https://github.com/user-attachments/assets/9e6e050d-c782-461b-8084-5ff6496d7bd9" />

Closes #3628

TODO in follow-up PRs:

- Add the ability to annotate API groups with supplementary content  (so we can have longer descriptions of complex APIs like Responses)
- Clean up docstrings to show API endpoints (or short semantic titles) in the sidebar

## Test Plan

- Local testing
- Made sure API conformance test still passes

docs/docs/api-overview.md

@@ -0,0 +1,49 @@
+# API Reference Overview
+
+The Llama Stack provides a comprehensive set of APIs organized by stability level to help you choose the right endpoints for your use case.
+
+## 🟢 Stable APIs
+
+**Production-ready APIs with backward compatibility guarantees.**
+
+These APIs are fully tested, documented, and stable. They follow semantic versioning principles and maintain backward compatibility within major versions. Recommended for production applications.
+
+[**Browse Stable APIs →**](./api/llama-stack-specification)
+
+**Key Features:**
+- ✅ Backward compatibility guaranteed
+- ✅ Comprehensive testing and validation
+- ✅ Production-ready reliability
+- ✅ Long-term support
+
+---
+
+## 🟡 Experimental APIs
+
+**Preview APIs that may change before becoming stable.**
+
+These APIs include v1alpha and v1beta endpoints that are feature-complete but may undergo changes based on feedback. Great for exploring new capabilities and providing feedback.
+
+[**Browse Experimental APIs →**](./api-experimental/llama-stack-specification-experimental-apis)
+
+**Key Features:**
+- 🧪 Latest features and capabilities
+- 🧪 May change based on user feedback
+- 🧪 Active development and iteration
+- 🧪 Opportunity to influence final design
+
+---
+
+## 🔴 Deprecated APIs
+
+**Legacy APIs for migration reference.**
+
+These APIs are deprecated and will be removed in future versions. They are provided for migration purposes and to help transition to newer, stable alternatives.
+
+[**Browse Deprecated APIs →**](./api-deprecated/llama-stack-specification-deprecated-apis)
+
+**Key Features:**
+- ⚠️ Will be removed in future versions
+- ⚠️ Migration guidance provided
+- ⚠️ Use for compatibility during transition
+- ⚠️ Not recommended for new projects

docs/docs/providers/agents/index.mdx

@@ -1,12 +1,7 @@
 ---
-description: "Agents API for creating and interacting with agentic systems.
+description: "Agents
 
-    Main functionalities provided by this API:
-    - Create agents with specific instructions and ability to use tools.
-    - Interactions with agents are grouped into sessions (\"threads\"), and each interaction is called a \"turn\".
-    - Agents can be provided with various tools (see the ToolGroups and ToolRuntime APIs for more details).
-    - Agents can be provided with various shields (see the Safety API for more details).
-    - Agents can also use Memory to retrieve information from knowledge bases. See the RAG Tool and Vector IO APIs for more details."
+    APIs for creating and interacting with agentic systems."
 sidebar_label: Agents
 title: Agents
 ---
@@ -15,13 +10,8 @@ title: Agents
 
 ## Overview
 
-Agents API for creating and interacting with agentic systems.
+Agents
 
-    Main functionalities provided by this API:
-    - Create agents with specific instructions and ability to use tools.
-    - Interactions with agents are grouped into sessions ("threads"), and each interaction is called a "turn".
-    - Agents can be provided with various tools (see the ToolGroups and ToolRuntime APIs for more details).
-    - Agents can be provided with various shields (see the Safety API for more details).
-    - Agents can also use Memory to retrieve information from knowledge bases. See the RAG Tool and Vector IO APIs for more details.
+    APIs for creating and interacting with agentic systems.
 
 This section contains documentation for all available providers for the **agents** API.