feat(app): add running status ring and lighten status dots

Keep the animated ring phase-locked across hosts and derive its knockout surface from each host's actual interaction state. Align filled status circles at 6px while preserving the larger needs-input alert.

Co-authored-by: Christoph Leiter <christoph@leiter.io>

packages/app/src/components/status-ring/index.tsx

@@ -0,0 +1,32 @@
+import { memo } from "react";
+import { View } from "react-native";
+import Animated, { useAnimatedStyle } from "react-native-reanimated";
+import {
+  StatusRingFrame,
+  type StatusRingProps,
+  rotatorStyles,
+  styles,
+} from "@/components/status-ring/frame";
+import { useStatusRingRotation } from "@/components/status-ring/clock";
+
+/**
+ * Native running indicator. The rotation is published by one shared UI-thread clock rather than
+ * per-instance timing, so a ring that mounts mid-flight is already in phase — see `clock.ts`.
+ *
+ * The rotated view carries no theme-tracked style; the coloured arc is nested inside it. Putting
+ * a Unistyles style on a Reanimated view crashes on theme change (docs/unistyles.md).
+ */
+export const StatusRing = memo(function StatusRing({ backdrop }: StatusRingProps) {
+  const rotation = useStatusRingRotation();
+  const rotatorStyle = useAnimatedStyle(() => ({
+    transform: [{ rotate: `${rotation.value}deg` }],
+  }));
+
+  return (
+    <StatusRingFrame backdrop={backdrop}>
+      <Animated.View style={[rotatorStyles.rotator, rotatorStyle]}>
+        <View style={styles.arc} />
+      </Animated.View>
+    </StatusRingFrame>
+  );
+});