docs(agent): fix README/API drift — ctx.local, StateAccessor, stream semantics

[LukasParke]

Three README sections document APIs that don't exist (each cost real debugging time building production agents on the SDK):

1. Tool Context: ctx?.context.… → actual API is ctx.local
2. Conversation State: state as mutable value + (await getResponse()).state → actual API is a StateAccessor ({load, save}), read via result.getState()
3. Streams: getToolStream() yields argument deltas (+ generator preliminary_result), not execution events — those are on getFullResponsesStream()

Corrected against source; added a streams cheat-sheet table; StateAccessor example notes plain-JSON serverless resume. Docs-only. Related: SDK-423/SDK-307.

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[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no bugs or issues to report.

[perry-the-pr-reviewer]

Perry's Review

Verdict: 💬 Comments / questions

(Posting as COMMENT, not APPROVE: the maintainer GitHub App lacks pull_requests:write on OpenRouterTeam, so Perry cannot record a formal approval here. Content-wise this is an LGTM — docs-only, no action items.)

Details

Accurate docs-only fix. I verified all three drift corrections against source at the PR head:

• ctx.local — the tool call context exposes local (a getter on the merged context object); the old ctx.context example was simply wrong. Corrected.
• StateAccessor + getState() — the state option takes a { load, save } accessor, and state is read via getState(). The old (await getResponse()).state was fiction — getResponse() returns an OpenResponsesResult with no state field. Corrected, and the plain-JSON serverless-resume note is accurate.
• Stream semantics — getToolStream() yields delta argument events plus preliminary_result for generator tools; execution results (tool.result / tool.call_output) ride getFullResponsesStream(). Both event names exist in source and the new cheat-sheet table matches the implementation.

The leftover createInitialState import in the Subpath Exports section is correct, not stale — that subpath export still exists. No changes requested.