docs: env vars inherited into CLI subprocess (filter list)

[tapheret2]

Summary

Actionable follow-up related to: docs: env vars inherited into CLI subprocess (filter list).

Why

Improves contributor onboarding and reduces repeated review questions.

Proposal

• Capture the missing guidance in docs (or a short CONTRIBUTING subsection)
• Include at least one concrete example or command
• Link from README if it is discoverability-related

Acceptance criteria

• Doc section exists and is linked
• Example is copy-pasteable
• No unrelated refactors in the implementing PR

Notes

Happy to implement if maintainers want this tracked as a good first issue.

[ondraulehla]

I traced the actual behavior in
_internal/transport/subprocess_cli.py::_spawn_process:

• the subprocess inherits the full parent os.environ, with exactly one key
  filtered out: CLAUDECODE (so SDK-spawned processes don't think they're
  nested inside a Claude Code parent, per Bug: Subprocess inherits CLAUDECODE=1 env var, preventing SDK usage from Claude Code hooks/plugins #573),
• the SDK then overlays CLAUDE_CODE_ENTRYPOINT (overridable), everything
  from ClaudeAgentOptions.env (user wins over inherited), and finally
  CLAUDE_AGENT_SDK_VERSION (always set by the SDK),
• plus conditional extras: CLAUDE_CODE_ENABLE_SDK_FILE_CHECKPOINTING, PWD,
  and fresh OTEL TRACEPARENT/TRACESTATE when a span is active.

Plan: add an "Environment variables" section to the README (near "Working
Directory") documenting the merge order as a short list, with a copy-pasteable
example showing how to override/blank sensitive inherited vars via
options.env, and a note that inheritance is allowlist-free — worth calling
out for anyone running agents on untrusted instructions. No code changes.

Will open a PR shortly unless someone's already on it.