Add TrustedRouter custom OpenAI client example

[jperla]

Summary

• document TrustedRouter as an OpenAI-compatible routing option
• use https://api.trustedrouter.com/v1 as the base URL
• include the trustedrouter/zdr model alias for privacy-sensitive agent workloads

Why

TrustedRouter is useful for workflows that involve private code, customer data, or other sensitive context. It provides open-source, verifiable attested routing and does not log prompts or outputs by default.

Validation

• git diff --check

---

Summary by cubic

Add a runnable TrustedRouter custom client example and document it in the README. Enables privacy-sensitive Stagehand workflows using trustedrouter/zdr via https://api.trustedrouter.com/v1.

• New Features
  • Added packages/core/examples/custom-client-trustedrouter.ts showing CustomOpenAIClient with trustedrouter/zdr and TRUSTEDROUTER_API_KEY.
  • Updated README with a short guide and link to the example.

^{Written for commit 7ddda6c. Summary will update on new commits.}

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[github-actions]

This PR is from an external contributor and must be approved by a stagehand team member with write access before CI can run.
Approving the latest commit mirrors it into an internal PR owned by the approver.
If new commits are pushed later, the internal PR stays open but is marked stale until someone approves the latest external commit and refreshes it.

[jperla]

Marked this ready for review. This is a docs/example-only TrustedRouter setup using the OpenAI-compatible endpoint at https://api.trustedrouter.com/v1; happy to adjust the example placement if the Stagehand team prefers another docs location.

[cubic-dev-ai]

No issues found across 2 files

Confidence score: 5/5

• Automated review surfaced no issues in the provided summaries.
• No files require special attention.

Architecture diagram

sequenceDiagram
    participant User as "User Script"
    participant Stagehand as Stagehand
    participant CustomClient as "CustomOpenAIClient"
    participant TR as "TrustedRouter API"

    Note over User,TR: NEW: TrustedRouter custom OpenAI client flow

    User->>Stagehand: new Stagehand({ llmClient: CustomOpenAIClient })
    User->>Stagehand: stagehand.init()

    User->>Stagehand: stagehand.act("click on the 'new' link")
    Stagehand->>CustomClient: send("click on the 'new' link")
    CustomClient->>TR: POST /v1/chat/completions\n(model: trustedrouter/zdr)
    TR-->>CustomClient: completion
    CustomClient-->>Stagehand: action result
    Stagehand-->>User: done

    User->>Stagehand: stagehand.extract("Extract the top 3 stories...")
    Stagehand->>CustomClient: extract request
    CustomClient->>TR: POST /v1/chat/completions\n(model: trustedrouter/zdr)
    TR-->>CustomClient: structured output
    CustomClient-->>Stagehand: parsed extraction
    Stagehand-->>User: headlines

    User->>Stagehand: stagehand.close()

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_{Re-trigger cubic}