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Four layers of visibility, from inside a call out to your dashboards.

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1. Live per-call metrics

Inside (or after) session.run(), take a CallMetrics snapshot: 
m = ctx.session.metrics.live()

m.turns           # int: dialog turns so far
m.duration_s      # float
m.stt_p95_ms      # int: P95 speech-to-text latency
m.llm_p95_ms      # int: P95 brain latency
m.tts_p95_ms      # int: P95 synthesis latency
m.cost.voice      # float - speech-stack cost
m.cost.llm        # float - model cost
m.cost.total      # float
m.tokens.input    # int
m.tokens.output   # int
m.active_llm      # str: model used on the last turn

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2. Stream metrics to your dashboard

The runner fires a metric event you can forward anywhere: 
@runner.on("metric")
async def _(ctx: CallContext, metric: CallMetrics) -> None:
    push_to_grafana(metric)

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3. Runner pool stats

s = runner.stats()        # RunnerStats snapshot

s.in_flight               # current active calls
s.queued                  # dispatches waiting for capacity
s.capacity                # your max_sessions setting
s.completed_last_hour
s.failed_last_hour
s.mean_call_duration_s
Poll this on a timer for liveness dashboards - see AgentRunner & Sessions.

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4. Post-call timing

After the call, the transcript carries a per-turn, per-stage latency breakdown (audio_ingress_ms, stt_ms, bridge_to_dev_ms, dev_brain_ms, tts_ms) - see Recordings & Transcripts.
High dev_brain_ms with healthy stt_ms/tts_ms means the latency is in YOUR brain - usually a stream() that is not actually streaming. See Streaming is the hot path.