[Docs] Integrations docs

[akeimach]

why

what changed

test plan

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Summary by cubic

Adds a new “Code mode” integration guide for Stagehand v4, with copy‑pasteable examples for MCP and non‑MCP agent SDKs. Adds an “Integrations” nav group so the page is easy to find. Supports STG-2568 by delivering runnable docs examples.

• New Features
  • New page: v4 Integrations → Code mode, explaining the code_execute tool and that the agent framework is the orchestrator.
  • MCP setup: stdio server command to load the tool; note to keep one session open so the browser persists.
  • Non‑MCP setup: TypeScript example using StagehandCodeExecutor and stagehandCodeConfigFromEnv, with execute(), metrics(), and clean shutdown.
  • Config: environment‑based selection of local or browserbase, provider keys, and model overrides.
  • Behavior: snippet API, return shape, limits, persistence between calls, abort semantics, and security caveats.
  • v4 guidance: include STAGEHAND_CODEMODE_SKILL/STAGEHAND_CODEMODE_REFERENCE to keep models on the supported API.
  • Notes that @browserbasehq/stagehand-integrations is private while the API settles.

^{Written for commit e379a84. Summary will update on new commits.}

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