feat(chat): live turn metrics — telemetry reducer + rendering

Consume wire/transport-contract 0.3.0 (step-complete event + timing
fields on usage/tool-result/done). Pure core/telemetry module:
foldMetricEvent (reducer) + derived selectors (stepTps, turnTps, etc).
TelemetryState is pure data, no active-turn tracking — consumers pass
turnId to selectors. ChatStore wires foldMetricEvent into handleDelta
and exposes telemetry + currentTurnId. ChatView shows step-metrics
footer (time/TPS/tokens) on assistant text bubbles and durationMs badge
on tool cards. New TurnSummary component renders turn-level stats
(wall-clock, tokens, steps, TPS) in a DaisyUI stats block. Extended
live-probe to verify telemetry events against bin/up (pending backend
restart). 336 tests, typecheck 0, biome clean, build ok.

1 files changed, 95 insertions, 0 deletions

diff --git a/src/core/telemetry/selectors.ts b/src/core/telemetry/selectors.ts
new file mode 100644
index 0000000..ecf1794
--- /dev/null
+++ b/src/core/telemetry/selectors.ts
@@ -0,0 +1,95 @@
+import type { Usage } from "@dispatch/wire";
+import type { StepMetrics, TelemetryState, TurnMetrics } from "./types";
+
+/** Get the metrics for a specific step within a turn. */
+export function stepMetrics(
+	state: TelemetryState,
+	turnId: string,
+	stepIndex: number,
+): StepMetrics | undefined {
+	return state.turns.get(turnId)?.steps[stepIndex];
+}
+
+/** Get the metrics for a turn. */
+export function turnMetrics(state: TelemetryState, turnId: string): TurnMetrics | undefined {
+	return state.turns.get(turnId);
+}
+
+/** The number of steps in a turn. */
+export function stepCount(state: TelemetryState, turnId: string): number {
+	return state.turns.get(turnId)?.steps.length ?? 0;
+}
+
+/** TTFT of the first step in a turn (the turn-visible first-token latency). */
+export function turnTtft(state: TelemetryState, turnId: string): number | undefined {
+	return state.turns.get(turnId)?.steps[0]?.ttftMs;
+}
+
+/** Sum of all steps' decode times in a turn. */
+export function totalDecodeMs(state: TelemetryState, turnId: string): number | undefined {
+	const steps = state.turns.get(turnId)?.steps;
+	if (steps === undefined || steps.length === 0) return undefined;
+	let total = 0;
+	let found = false;
+	for (const s of steps) {
+		if (s.decodeMs !== undefined) {
+			total += s.decodeMs;
+			found = true;
+		}
+	}
+	return found ? total : undefined;
+}
+
+/** Aggregate output tokens across all steps in a turn. */
+export function totalOutputTokens(state: TelemetryState, turnId: string): number | undefined {
+	const turn = state.turns.get(turnId);
+	if (turn === undefined) return undefined;
+	if (turn.doneUsage !== undefined) return turn.doneUsage.outputTokens;
+	let total = 0;
+	let found = false;
+	for (const s of turn.steps) {
+		if (s.usage?.outputTokens !== undefined) {
+			total += s.usage.outputTokens;
+			found = true;
+		}
+	}
+	return found ? total : undefined;
+}
+
+/** Aggregate input tokens across all steps in a turn. */
+export function totalInputTokens(state: TelemetryState, turnId: string): number | undefined {
+	const turn = state.turns.get(turnId);
+	if (turn === undefined) return undefined;
+	if (turn.doneUsage !== undefined) return turn.doneUsage.inputTokens;
+	let total = 0;
+	let found = false;
+	for (const s of turn.steps) {
+		if (s.usage?.inputTokens !== undefined) {
+			total += s.usage.inputTokens;
+			found = true;
+		}
+	}
+	return found ? total : undefined;
+}
+
+/** Derived TPS for a step: outputTokens / (decodeMs / 1000). */
+export function stepTps(step: StepMetrics): number | undefined {
+	if (step.usage?.outputTokens === undefined || step.decodeMs === undefined) return undefined;
+	if (step.decodeMs === 0) return undefined;
+	return step.usage.outputTokens / (step.decodeMs / 1000);
+}
+
+/** Derived aggregate TPS for a turn. */
+export function turnTps(state: TelemetryState, turnId: string): number | undefined {
+	const outTokens = totalOutputTokens(state, turnId);
+	const decode = totalDecodeMs(state, turnId);
+	if (outTokens === undefined || decode === undefined || decode === 0) return undefined;
+	return outTokens / (decode / 1000);
+}
+
+/** Sum of tool execution durations within a step. */
+export function stepToolDuration(step: StepMetrics): number | undefined {
+	return step.toolDurationMs !== undefined && step.toolDurationMs > 0
+		? step.toolDurationMs
+		: undefined;
+}