feat: OTEL metrics for latencies, usage, and connection timing

[theomonnom]

Adds OTEL metrics export to LiveKit Cloud via OTLP.

Turn latency histograms (per-turn, keyed by model_name / model_provider)

• lk.agents.turn.e2e_latency — end-to-end turn latency
• lk.agents.turn.llm_ttft — LLM time to first token
• lk.agents.turn.tts_ttfb — TTS time to first byte
• lk.agents.turn.transcription_delay — time from end of speech to transcript
• lk.agents.turn.end_of_turn_delay — time from end of speech to turn decision
• lk.agents.turn.on_user_turn_completed_delay — time in on_user_turn_completed callback

Usage counters (per-event, keyed by model_name / model_provider)

• lk.agents.usage.llm_input_tokens — LLM input tokens
• lk.agents.usage.llm_input_cached_tokens — LLM cached input tokens
• lk.agents.usage.llm_output_tokens — LLM output tokens
• lk.agents.usage.llm_input_audio_tokens — LLM input audio tokens
• lk.agents.usage.llm_input_text_tokens — LLM input text tokens
• lk.agents.usage.llm_output_audio_tokens — LLM output audio tokens
• lk.agents.usage.llm_output_text_tokens — LLM output text tokens
• lk.agents.usage.llm_session_duration — LLM session duration (for session-based billing)
• lk.agents.usage.tts_characters — TTS characters synthesized
• lk.agents.usage.tts_audio_duration — TTS audio duration
• lk.agents.usage.stt_audio_duration — STT audio duration
• lk.agents.usage.interruption_num_requests — interruption detection requests

Connection histogram (per-event, keyed by model_name / model_provider / connection_reused)

• lk.agents.connection.acquire_time — time to acquire a WebSocket connection

Other changes

• Added MetricsMetadata TypedDict (model_name/model_provider) to MetricsReport for per-component model info (llm_metadata, tts_metadata, stt_metadata)
• Added acquire_time and connection_reused fields to STTMetrics, TTSMetrics, RealtimeModelMetrics
• ConnectionPool tracks last_acquire_time / last_connection_reused
• Wired up connection timing in all STT, TTS, and realtime plugins
• Compact __repr__ on all metrics types (skip default fields)
• Set up OTEL MeterProvider with OTLP exporter for Cloud
• Usage counters added directly per-event (no buffering)

Not included

• Realtime model metadata on turn histograms (needs different naming since one model covers the whole pipeline)

[devin-ai-integration]

Devin Review found 1 new potential issue.

View 14 additional findings in Devin Review.

[devin-ai-integration]

🟡 ConnectionPool stores timing info in shared mutable state, creating a race between concurrent callers

ConnectionPool.last_acquire_time and last_connection_reused are instance-level attributes set inside get() (under _connect_lock) but read by callers after the lock is released. In asyncio, the pattern async with pool.connection(...) as ws: self._x = pool.last_acquire_time is safe only because there's no await between yield and the read. However, this is fragile: any future refactor that adds an await between the context manager entry and the read would silently corrupt the values. A more robust design would return the timing info from get()/connection() directly, as ElevenLabs' _current_connection() does (returning a tuple).

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