Why

core/src/goals.rs already emits OTEL metrics for goal creation, resume, terminal transitions, token counts, and duration. As /goal moves into ext/goal, the extension needs to preserve that telemetry contract instead of only emitting app-visible ThreadGoalUpdated events.

This keeps the existing codex.goal.* metric surface intact while goal lifecycle ownership shifts toward the extension.

What changed

• Added an extension-local GoalMetrics helper that records the existing codex.goal.* counters and histograms through codex-otel.
• Threaded an optional MetricsClient through install_with_backend, GoalExtension, GoalRuntimeHandle, and GoalToolExecutor.
• Emitted created, resumed, and terminal goal metrics from the extension paths that create goals, restore active goals on thread resume, account budget limits, complete or block goals, and handle external goal mutations.
• Updated existing goal extension test setup callsites to pass None for metrics when instrumentation is not under test.

Verification

Not run locally.