docs: add OpenTelemetry provider guides

[antonvishal]

Summary

Adds Stagehand v4 OTLP setup guides for Braintrust, Langfuse, LangSmith, Sentry, and the OpenTelemetry Collector.

• Adds an overview of Stagehand's trace format and provider options.
• Includes TypeScript, Python, and Go examples with verification steps for each provider.
• Documents the base OpenTelemetry Collector setup for routing or transcoding traces.
• Adds provider navigation, logos, and a link from the observability configuration page.

I manually verified the endpoint and header requirements for each provider.

Follow-up: add a Stagehand page to each provider's documentation.

Test plan

• Formatting check
• Docs unit tests, 27 passed

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Latest commit: 5bcbd46

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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.

[Kylejeong2]

@cubic review

[cubic-dev-ai]

@cubic review

@Kylejeong2 I have started the AI code review. It will take a few minutes to complete.

[Kylejeong2]

left some comments, address @cubic as well

[cubic-dev-ai]

All reported issues were addressed across 12 files

Architecture diagram

sequenceDiagram
    participant Dev as Developer
    participant App as Stagehand App
    participant Browser as Local Browser
    participant OTel as OTLP Exporter
    participant Provider as Observability Provider
    participant Collector as OTel Collector

    Note over Dev,Provider: Stagehand v4 OpenTelemetry Integration Flow

    Dev->>App: launch() + create() with telemetry config
    App->>Browser: Start browser context
    App->>App: Emit operation spans (act/observe/extract)
    App->>App: Emit log spans for each log record
    Browser-->>App: Page interaction results

    App->>OTel: Batched OTLP/HTTP JSON export to /v1/traces
    
    alt Direct provider export
        OTel->>Provider: POST traces with provider-specific headers
        Note over OTel,Provider: Auth varies by provider
        alt Braintrust
            OTel->>Provider: Authorization: Bearer + x-bt-parent: project_id
        else Langfuse
            OTel->>Provider: Authorization: Basic + x-langfuse-ingestion-version: 4
        else LangSmith
            OTel->>Provider: x-api-key + Langsmith-Project header
        else Sentry
            OTel->>Provider: x-sentry-auth: sentry sentry_key
        end
        Provider-->>OTel: 200 OK / export error
    else Collector routing (NEW: OTLP Collector)
        OTel->>Collector: POST http://localhost:4318/v1/traces
        Collector->>Collector: Batch processor + fan-out
        Collector->>Provider: Export via otlp_http exporter
        Provider-->>Collector: Response
        Collector-->>OTel: 200 / error
    end

    Note over App,Provider: Verification
    Provider->>Provider: File trace under project (x-bt-parent, Langsmith-Project, etc.)
    Dev->>Provider: Check traces with service.name = stagehand-service-worker

    alt Missing traces
        Note over Dev,Provider: Check data plane/region, headers, and close() was called
    end

    App->>App: stagehand.close() flushes remaining batch
    App->>OTel: Final export before process exit

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[antonvishal]

Hey @Kylejeong2, I addressed the comments.