fix(agents): persist _speech_start_time across intra-turn VAD bursts

[AlessandroElyos]

Within a single user turn, VAD can fire multiple START_OF_SPEECH/END_OF_SPEECH cycles separated by short silences (e.g. the user says "Hello." then pauses briefly before continuing). End-of-turn detection is decoupled from VAD — a turn is only considered ended once _bounce_eou_task runs and clears the per-turn state.

_vad_speech_started was being reset to False in the END_OF_SPEECH branch of _on_vad_event. The next START_OF_SPEECH within the same turn would therefore overwrite _speech_start_time with the latest burst's start, losing the original turn-start timestamp. This propagates to started_speaking_at on the EOT metrics report, which downstream consumers (recording-to-transcript alignment, analytics) rely on to know when the user actually began speaking.

The fix removes the _vad_speech_started = False reset from the END_OF_SPEECH branch. The flag is now cleared only by the EOT cleanup in _bounce_eou_task — which is already the lifecycle owner of _speech_start_time — so both fields are governed symmetrically by turn boundaries rather than burst boundaries.

_vad_speech_started is read at exactly one site (the SOS guard) and is also defensively reset in the VAD task finally block on handoff/teardown, so removing the EOS reset has no other side effects.

Adds tests/test_speech_start_time_persistence.py with three cases following the existing test_audio_recognition_aclose.py style:

• test_first_sos_sets_speech_start_time — sanity check.
• test_speech_start_time_persists_across_intra_turn_bursts — the bug reproducer; fails before the fix, passes after.
• test_eos_does_not_clear_vad_speech_started — encodes the new invariant.

[devin-ai-integration]

✅ Devin Review: No Issues Found

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[AlessandroElyos]

The failing test_interruption_before_speaking[True-3.5] looks like a pre-existing flake unrelated to this PR — it's a timing-sensitive assertion (5× speed factor, 0.75s tolerance on check_timestamp). I ran it 3× locally with the fix applied and it passed each time. Happy to fix it if it can help

[longcw]

this makes the _speech_start_time always the turn start time, may break the tracing that we create user_speaking spans using this timestamp as the start of the span (ref).

using the start time of the user_turn_span could be a better solution if the goal is to make started_speaking_at in the EOT info the first time user started speaking. we already have _ensure_user_turn_span that create the span only when there is no active user turn span, and the span is ended only after EOT committed.

the OTEL span is designed for write-only, so maybe add a _user_turn_start alongside the user_turn_span.

[AlessandroElyos]

thanks for the feedback @longcw.

I reverted the change on _vad_speech_started.

I also added a _user_turn_start variable as you suggested that should reflect the actual turn boundaries.

Let me know your thoughts.