docs: sync code blocks and generate API reference

sdk/api-reference/openhands.sdk.workspace.mdx

@@ -302,6 +302,10 @@ as it provides better isolation and security.
 
 #### Properties
 
+- `alive`: bool
+  Check if the remote workspace is alive by querying the health endpoint.
+  * Returns:
+    True if the health endpoint returns a successful response, False otherwise.
 - `api_key`: str | None
 - `client`: Client
 - `host`: str

sdk/guides/agent-server/cloud-workspace.mdx

@@ -20,7 +20,7 @@ This example demonstrates using OpenHandsCloudWorkspace to provision a sandbox
 via OpenHands Cloud (app.all-hands.dev) and run an agent conversation.
 
 Usage:
-  uv run examples/02_remote_agent_server/07_convo_with_cloud_workspace.py
+  uv run examples/02_remote_agent_server/06_convo_with_cloud_workspace.py
 
 Requirements:
   - LLM_API_KEY: API key for direct LLM provider access (e.g., Anthropic API key)

sdk/guides/agent-server/custom-tools.mdx

@@ -23,7 +23,7 @@ by building a custom base image that includes the tool implementation.
 
 Prerequisites:
     1. Build the custom base image first:
-       cd examples/02_remote_agent_server/06_custom_tool
+       cd examples/02_remote_agent_server/05_custom_tool
        ./build_custom_image.sh
 
     2. Set LLM_API_KEY environment variable

sdk/guides/skill.mdx

@@ -173,14 +173,14 @@ tools = [
 agent_context = AgentContext(
     skills=[
         Skill(
-            name="AGENTS.md",
+            name="repo.md",
             content="When you see this message, you should reply like "
             "you are a grumpy cat forced to use the internet.",
             # source is optional - identifies where the skill came from
             # You can set it to be the path of a file that contains the skill content
             source=None,
             # trigger determines when the skill is active
-            # trigger=None means always active
+            # trigger=None means always active (repo skill)
             trigger=None,
         ),
         Skill(
@@ -366,7 +366,15 @@ AgentSkills standard which includes:
 - SKILL.md file with frontmatter metadata (name, description, triggers)
 - Optional resource directories: scripts/, references/, assets/
 
-See the example_skills/ directory for a complete skill structure.
+The example_skills/ directory contains two skills:
+- rot13-encryption: Has triggers (encrypt, decrypt) - listed in <available_skills>
+  AND content auto-injected when triggered
+- code-style-guide: No triggers - listed in <available_skills> for on-demand access
+
+All SKILL.md files follow the AgentSkills progressive disclosure model:
+they are listed in <available_skills> with name, description, and location.
+Skills with triggers get the best of both worlds: automatic content injection
+when triggered, plus the agent can proactively read them anytime.
 """
 
 import os
@@ -420,7 +428,7 @@ def main():
     if agent_skills:
         skill_name = list(agent_skills.keys())[0]
         loaded_skill = agent_skills[skill_name]
-        print("\nLoaded skill details (AgentSkills standard fields):")
+        print(f"\nDetails for '{skill_name}' (AgentSkills standard fields):")
         print(f"  - Name: {loaded_skill.name}")
         desc = loaded_skill.description or ""
         print(f"  - Description: {desc[:70]}...")
@@ -455,6 +463,7 @@ def main():
         usage_id="skills-demo",
         model=model,
         api_key=SecretStr(api_key),
+        base_url=os.getenv("LLM_BASE_URL"),
     )
 
     # Create agent context with loaded skills