docs: add deployment field documentation for agent dispatch

[xianshijing-lk]

Summary

• Update docstrings to document the deployment field in create_dispatch
• Update agent_dispatch example to support the --deployment argument
• Add changeset

The deployment field allows targeting a specific agent deployment (e.g., "staging"). Leave empty to target the production deployment.

Related PRs:

• node-sdks: Add deployment to CreateDispatchOptions node-sdks#675
• python-sdks: docs: add deployment field documentation for agent dispatch python-sdks#722
• client-sdk-js: Add deployment to TokenSourceFetch options client-sdk-js#1971

Test plan

Unit Tests

cd /path/to/rust-sdks
cargo test -p livekit-api

Manual Verification

1. Run example with deployment flag:

cd examples/agent_dispatch
cargo run -- \
  --url $LIVEKIT_URL \
  --key $LIVEKIT_API_KEY \
  --secret $LIVEKIT_API_SECRET \
  --room-name test-room \
  --agent-name my-agent \
  --deployment staging

2. Verify response contains deployment:

let dispatch = client.create_dispatch(CreateAgentDispatchRequest {
    agent_name: "my-agent".into(),
    room: "test-room".into(),
    deployment: "staging".into(),
    ..Default::default()
}).await?;

println!("Dispatch ID: {}", dispatch.id);
println!("Deployment: {}", dispatch.deployment);  // Should print "staging"

3. Verify via list_dispatch:

let dispatches = client.list_dispatch("test-room").await?;
for d in dispatches {
    println!("Dispatch {}: deployment={}", d.id, d.deployment);
}

End-to-End Verification

1. Register an agent worker with deployment="staging"
2. Create a dispatch targeting deployment="staging" using the example
3. Verify only the staging agent receives the job

🤖 Generated with Claude Code

[github-actions]

Changeset

The following package versions will be affected by this PR:

Package	Bump
"livekit-api"	patch