fix: preserve adaptive interruption across tool calls

[chenghao-mou]

Bug: Adaptive interruption could silently drop a user overlap when agent playout resumed after a tool call because the interruption stream received mismatched speech boundaries.

Treat thinking gaps as real speech boundaries and restart overlap inference when playout resumes mid-utterance. Agent-ended overlaps remain inconclusive and no longer count as backchannels; remote forwarding is noted until the protocol carries that marker.

Fixes #6548. Fixes #6548.

[devin-ai-integration]

✅ Devin Review: No Issues Found

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

[biztex]

This looks like the right fix — treating the thinking gap as a real speech boundary and restarting overlap inference when playout resumes addresses the root cause at the signal source, where my #6550 only made the stream tolerate the redundant start sentinel. The metrics and remote-session coverage go beyond what mine attempted, too.

Closing #6550 in favor of this. If the hermetic stream-level regression tests from it would be useful here (a fake bargein gateway driving InterruptionWebSocketStream through a mid-overlap second segment), happy to adapt them to the new sentinel semantics — just say the word.

[longcw]

question: what is the difference between session.agent_state and self._agent_speaking?

[biztex]

(Chiming in from #6550, since this distinction was the heart of #6548 — hope it helps.)

They live at different layers and deliberately diverge mid-turn:

• session.agent_state is the session-level lifecycle (listening / thinking / speaking), updated via AgentActivity._update_agent_state(). A reply that produces tool calls flips it to "thinking" between segments; it is what applications observe through agent_state_changed.

• AudioRecognition._agent_speaking is a private recognition-side flag meaning "an agent playout window is open for interruption/endpointing purposes". It is set by _on_start_of_agent_speech() (first audio frame of playout) and cleared only inside _on_end_of_agent_speech() — which is intentionally not called when the reply produced tool calls, so it stays True straight through the thinking gap. It gates overlap tracking in _on_start_of_speech(), the transcript-ignore window, and _should_ignore_input_audio().

So during a tool-call gap the two disagree by design: agent_state == "thinking" while _agent_speaking == True. was_speaking as written captures "playout was audibly active at reply-done" (session view) rather than "the recognition-side speech window is still open" — which one is wanted here is of course the author's call.