fix(interruption): keep an open overlap when a second agent speech segment starts

[biztex]

Fixes #6548

Problem

One agent turn can span several speech segments: a reply that produces tool calls deliberately skips _on_end_of_agent_speech, so the follow-up tool-response reply (or a queued say()) raises _AgentSpeechStartedSentinel a second time with no end sentinel in between. _forward_data treated every start sentinel as a brand-new turn and called _reset_state(), clearing _overlap_started while the user was mid-interruption.

From that moment the interruption is silently swallowed:

• _overlap_started gates whether user audio is forwarded to the bargein gateway at all, so classification stops;
• the flag can only be raised again by _OverlapSpeechStartedSentinel, which only comes from a fresh VAD speech onset — and VAD does not re-announce speech that is already under way;
• at _OverlapSpeechEndedSentinel the event emission is behind if self._overlap_started, so no OverlappingSpeechEvent is emitted and AgentActivity.on_interruption never runs. The agent talks straight through the user.

Fix

Skip the reset when the stream already believes the agent is speaking and an overlap is open — i.e. treat the sentinel as a continuation of the same turn. The guard is deliberately narrow: a genuine new turn (an end sentinel was seen, so _agent_speech_started is False) still wipes the overlap, the audio buffer, the cache and the counters.

This ports the stream-side guard from the JS fix (livekit/agents-js#2117). The other half of that PR — restoring overlap state on a transport-failover replacement stream — does not apply to Python: these flags live on self and _run() reconnects in place on the same stream object.

Tests

New tests/test_interruption/test_interruption_overlap_state.py (unit, hermetic — fake gateway WS that answers every batch), ported from the JS PR's regression suite:

• test_second_speech_segment_keeps_open_overlap — user audio keeps reaching the gateway after a mid-overlap second segment, and the end-of-overlap event still surfaces with num_requests > 0 (fails on main)
• test_bargein_verdict_after_second_speech_segment — a bargein_detected response after the second segment still produces is_interruption=True (fails on main)
• test_new_agent_turn_still_resets_overlap_state — a genuine new turn still resets: audio stays gated until a fresh overlap opens (passes on main and with the fix — pins the guard's narrowness)

Verification: full --unit suite passes (1274 passed), ruff format --check / ruff check clean, mypy strict clean.

🤖 Generated with Claude Code

[CLAassistant]

All committers have signed the CLA.

[devin-ai-integration]

✅ Devin Review: No Issues Found

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

[biztex]

TL;DR for reviewers

One agent turn can span several speech segments (the reply after a tool call, or a queued say()). The second segment's start sentinel used to hit _reset_state() mid-overlap, which silently dropped an in-progress user barge-in: audio stopped reaching the classifier, the flag could never re-arm (VAD does not re-announce ongoing speech), and no verdict was emitted — the agent talked straight through the user.

The change is a narrow continuation guard in _forward_data (mirrors the JS fix in livekit/agents-js#2117), plus three hermetic regression tests: audio keeps flowing across a second segment, a bargein verdict still surfaces afterwards, and a genuine new turn still resets everything.

Status: all checks green, CLA signed, no open review threads. Happy to adjust anything.

[biztex]

Superseded by #6564, which fixes the root cause at the signal source (real speech boundaries around the thinking gap, restarting overlap inference on resume) and also covers the backchannel-metrics and remote-session angles. Closing in its favor.