Keep the Cursor stream open across tool round trips

[Yuki13929]

Summary

Agent loops (Claude Code) used to stall because every tool_result request opened a new Cursor turn and pasted the whole conversation back as flattened Human:/Assistant: text. Cursor's harness reads that as a forged transcript, so the model re-verified earlier steps, sometimes refused, and each round trip re-paid the ~25k token system prompt.

Now a tool_use keeps its upstream stream alive and the next request answers on it:

# server.py
tool_use -> remember_session(session, [block]); keep_open = True   # do not close()

Turn.start():
    if self._resume():        # tool_result ids -> the stream that emitted them
        return                # session.send_tool_results(...) on the same turn
    ... render_history(...)   # only when that stream is gone

_live maps tool_use.id -> (session, exec_id), is reaped after CURSOR2API_RESUME_TTL (900s), and only resumes when all returned ids belong to the same stream — otherwise it falls back to replay. The replay path now labels the history as relayed context (TRANSCRIPT_HEADER) instead of a raw chat log.

Also here: response_format (json_object / json_schema) emulated with an instruction plus incremental code-fence stripping (Unfence, streaming-safe), comma-separated local API_KEYs, .env, Docker files, and tests/test_units.py (19 cases, no network).

Measured with real Claude Code 2.1.197: a fix-bug + run-command task finishes in ~27s (previously hit the 200s timeout), and a 379-line file write completes in ~67s with no mid-task disconnect. tests/test_api.py and tests/test_openai.py both exit 0.