feat(omo-codex): wire Codex SessionStart telemetry for DAU/WAU/MAU

Adds a new Codex plugin component `telemetry` that emits a single
omo_codex_daily_active event (reason: session_start) from every Codex
SessionStart hook, with the same UTC-day deduplication, hashed
installation identifier, and four-flag opt-out as the install-time
event. Previously omo-codex telemetry only fired on install_completed,
so DAU/WAU/MAU under-reported real Codex usage.

- New plugin component packages/omo-codex/plugin/components/telemetry/
  mirrors the rules/comment-checker/lsp pattern: own src/, tsc build,
  vitest tests, package.json (posthog-node dep), hooks/hooks.json.
- src/codex-hook.ts wraps createPluginPostHog().trackActive(..., "session_start")
  with safeShutdown so Codex session startup never blocks on telemetry.
- Plugin root hooks.json + workspaces register the new component
  alongside rules and ultrawork on SessionStart.
- Aggregate test expectations updated to include the telemetry directory.
- cross-package-equivalence.test.ts pins product-identity constants and
  shouldDisablePostHog behavior to stay byte-equivalent between the CLI
  installer (src/telemetry/) and the plugin runtime
  (plugin/components/telemetry/src/), so the two PostHog sources never
  drift on event name, distinct_id base, dedup file path, or opt-out
  flags.
- PostHogActivityReason union in the CLI-side posthog.ts gains
  "session_start" so future CLI paths can emit the same reason without
  a type break.

packages/omo-codex/plugin/components/telemetry/src/posthog-activity-state.ts

@@ -0,0 +1,79 @@
+import { existsSync, mkdirSync, readFileSync } from "node:fs";
+import { join } from "node:path";
+
+import { writeFileAtomically } from "./atomic-write.js";
+import { getActivityStateDir } from "./data-path.js";
+
+export type PostHogActivityState = {
+	readonly lastActiveDayUTC?: string;
+};
+
+export type PostHogActivityCaptureState = {
+	readonly dayUTC: string;
+	readonly captureDaily: boolean;
+};
+
+const POSTHOG_ACTIVITY_STATE_FILE = "posthog-activity.json";
+
+function getPostHogActivityStateFilePath(): string {
+	return join(getActivityStateDir(), POSTHOG_ACTIVITY_STATE_FILE);
+}
+
+function getUtcDayString(date: Date): string {
+	return date.toISOString().slice(0, 10);
+}
+
+function isPostHogActivityState(value: unknown): value is PostHogActivityState {
+	return value !== null && typeof value === "object" && !Array.isArray(value);
+}
+
+function readPostHogActivityState(): PostHogActivityState {
+	const stateFilePath = getPostHogActivityStateFilePath();
+
+	if (!existsSync(stateFilePath)) {
+		return {};
+	}
+
+	try {
+		const stateContent = readFileSync(stateFilePath, "utf-8");
+		const stateJson: unknown = JSON.parse(stateContent);
+
+		if (!isPostHogActivityState(stateJson)) {
+			return {};
+		}
+
+		return stateJson;
+	} catch {
+		return {};
+	}
+}
+
+function writePostHogActivityState(nextState: PostHogActivityState): void {
+	const stateDir = getActivityStateDir();
+	const stateFilePath = getPostHogActivityStateFilePath();
+
+	try {
+		mkdirSync(stateDir, { recursive: true });
+		writeFileAtomically(stateFilePath, `${JSON.stringify(nextState, null, 2)}\n`);
+	} catch {
+		return;
+	}
+}
+
+export function getPostHogActivityCaptureState(now: Date = new Date()): PostHogActivityCaptureState {
+	const state = readPostHogActivityState();
+	const dayUTC = getUtcDayString(now);
+	const captureDaily = state.lastActiveDayUTC !== dayUTC;
+
+	if (captureDaily) {
+		writePostHogActivityState({
+			...state,
+			lastActiveDayUTC: dayUTC,
+		});
+	}
+
+	return {
+		dayUTC,
+		captureDaily,
+	};
+}