[Epic] Implement the Hosted Agent Invocations protocol

[shibayan]

Priority

P1 for HTTP; P3 for WebSocket and realtime scenarios.

Goal

Add the Foundry Hosted Agent Invocations protocol so TypeScript agents can accept arbitrary payloads and non-conversational workloads in addition to Responses API requests.

Scope

• HTTP invocation request routing, validation, execution, and response mapping.
• Shared invocation contracts and conformance tests.
• WebSocket invocation support for duplex and realtime scenarios.

Exit criteria

• Hosted agents can be invoked through the documented HTTP protocol.
• Protocol errors and cancellation have defined behavior.
• WebSocket support is independently testable and does not regress HTTP hosting.

Implementation is tracked by the sub-issues.