refactor(client): extract interval logic to a composable function

あと`onUnmounted`を`onMounted`内で呼んでいたりしたのを修正したりとか

packages/client/src/scripts/use-interval.ts

@@ -0,0 +1,22 @@
+import { onMounted, onUnmounted } from 'vue';
+
+export function useInterval(fn: () => void, interval: number, options: {
+	immediate: boolean;
+	afterMounted: boolean;
+}): void {
+	let intervalId: number | null = null;
+
+	if (options.afterMounted) {
+		onMounted(() => {
+			if (options.immediate) fn();
+			intervalId = window.setInterval(fn, interval);
+		});
+	} else {
+		if (options.immediate) fn();
+		intervalId = window.setInterval(fn, interval);
+	}
+
+	onUnmounted(() => {
+		if (intervalId) window.clearInterval(intervalId);
+	});
+}