feat(evals): run v4_code through shared MCP

[shrey150]

Why

This PR proves that the Claude Code v4_code eval path can consume the shared Stagehand code-mode MCP product instead of owning a separate executor and browser lifecycle.

Dependency shape

This is a two-file consumer fork with two logical dependencies:

• feat(evals): add AI-enabled V4 code surface #2378 provides the eval framework and AI harness this adapter modifies.
• feat: scaffold Stagehand code-mode MCP host #2597, feat: add Stagehand code execution tool #2619, and feat: add Stagehand code-mode guidance #2620 provide the shared package host, code_execute runtime, and canonical guidance.

It remains based on #2378 so the public diff contains only the consumer adapter and its tests. Making it a literal linear child of #2620 would also pull the independent eval stack into the package stack. The eval base must be refreshed with the package stack before merge.

What changed

• routes the Claude Code v4_code surface through the shared @browserbasehq/stagehand-integrations stdio server
• exposes mcp__stagehand_browser__code_execute as its browser execution tool
• maps eval startup profiles to explicit local or Browserbase STAGEHAND_BROWSER configuration
• installs the package's canonical SKILL.md and REFERENCE.md into a temporary Claude Code project skill
• limits the agent to the skill loader, shell, and shared code-execution tool
• leaves the deterministic V4 surface unchanged

Stagehand operation-metric capture remains deferred until the shared MCP contract exposes a metrics snapshot. This adapter does not recreate an eval-owned executor or browser lifecycle to collect it.

E2E Test Matrix

Command / flow	Observed output	Confidence / sufficiency
Locally built v4_code adapter with explicit local startup and a real Claude Code agent	Loaded the stagehand-v4-code project skill, called mcp__stagehand_browser__code_execute, read Example Domain from https://example.com, completed successfully, and left zero MCP/eval child processes. Browserbase credentials remained present during the run.	Proves explicit local startup wins even when remote credentials exist and exercises the consumer end to end.
Locally built v4_code adapter with Browserbase startup and a real Claude Code agent	Reported Browserbase configuration, loaded the project skill, called code_execute, read Example Domain, completed successfully, and left zero new running Browserbase sessions.	Exercises remote provisioning and task-scoped shutdown through the shared stdio MCP path.
pnpm exec vitest run --root . packages/evals/tests/framework/claudeCodeToolAdapter.test.ts packages/evals/tests/framework/claudeCodeRunner.test.ts	2 test files and 35 tests passed.	Covers adapter/profile configuration and guards the existing Claude Code runner contract.
pnpm --filter @browserbasehq/stagehand-evals typecheck && pnpm --filter @browserbasehq/stagehand-evals build	TypeScript completed without errors; both ESM and CLI builds completed.	Confirms the exact eval package under review compiles into both build targets.
pnpm exec oxfmt --check packages/evals/framework/claudeCodeToolAdapter.ts packages/evals/tests/framework/claudeCodeToolAdapter.test.ts	Both files passed formatting.	Supporting source-format check.

Changeset

None. This changes eval-harness and test plumbing rather than a published package.

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Latest commit: 32653f1

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