fix(voice): scope playout state per generation step in SpeechHandle

[anshulkulhari7]

Summary

Follow-up to #5594 (the cross-step stale-paused-speech fix).

SpeechHandle is the public whole-turn handle, but a multi-step turn reuses the
same handle across generation steps while some state (playout / pause) is
generation-step local. #5594 resets _paused_speech in _scheduling_task after
the current generation's _wait_for_generation completes, which covers the
cross-step leak. It does not cover the case @jayeshp19 flagged in #5533:

the false-interruption timer fires before the silent tool-call generation
finishes. In that case the runtime can still do a thinking → listening → thinking false-resume during the silent step itself … the pause-on-thinking
path can still record _paused_speech.

This is the "pausing while no audio is actually playing" edge case, and it is what
issue #5545 proposes to fix by scoping playout/pause state per generation step.

The bug (reproduced)

1. User asks "what's the weather in Tokyo?"
2. The model emits only a function call — a silent tool-call step, no audio.
3. VAD-only speech starts and ends during that silent step, so the pause-on-thinking
   path records _paused_speech and the false-interruption timer is scheduled.
4. The timer fires while the silent step is still active (before it advances to
   the tool reply).

On main, _on_false_interruption resumes and emits
AgentFalseInterruptionEvent(resumed=True) even though no audio ever played for
this step — leaking stale per-step playout state. The added regression test
asserts no such resume is emitted; it fails on main:

>       assert not any(ev.resumed for ev in false_interruption_events)
E       assert not True
tests/test_agent_session.py: AssertionError

Approach

Mirroring the issue's proposal ("a private generation-step ref … playout callbacks,
pause state, and cleanup timers should only mutate state when their captured
generation ref still matches the handle's current generation"), this scopes playout
state to the current step:

• SpeechHandle._playout_started — set when the current step starts audio playout
  (in the existing _on_first_frame callbacks), reset on every step advance
  (_authorize_generation). It records whether the current step is actually
  playing audio.
• _on_false_interruption now only treats a pause as a resumable false interruption
  when the current step actually started playout. For a silent step it undoes the
  preemptive pause silently and emits no resume event.

The change is additive and backward-compatible. The existing #5594 regression test
(test_silent_tool_call_pause_state_does_not_leak_into_tool_reply) and the rest of
the interruption suite still pass, since a real tool reply has started playout by the
time its timer fires.

Question for maintainers

@longcw @davidzhao — does this per-step _playout_started gating match the internal
direction you intended for #5545? I kept it minimal (a per-step playout flag + a
single early-return in the false-interruption timer) rather than introducing a
broader public per-step handle. Happy to fold playout-state tracking more fully into
a generation-step ref if you'd prefer that shape.

Verification

• uv run pytest tests/test_agent_session.py --unit — 34 passed (incl. new test and
  the fix: clear stale paused speech state across generation steps #5594 regression test)
• uv run ruff check / ruff format --check — clean on changed files
• uv run mypy -p livekit.agents (strict) — Success, no issues

Closes #5545

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AI-assisted: implemented with AI assistance; all changes were reviewed, tested, and verified by the author.

[devin-ai-integration]

✅ Devin Review: No Issues Found

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