fix(wake-lock): allow display sleep during active work

Prevent idle system sleep on supported desktop runtimes without intentionally keeping the display awake. Narrow wake-lock activation to true active work states and drop the web screen-wake fallback where the platform cannot provide system-sleep-only behavior.

packages/ui/src/stores/session-status.ts

@@ -1,11 +1,27 @@
 import type { Session, SessionRetryState, SessionStatus } from "../types/session"
 import { getInstanceSessionIndicatorStatusCached, sessions } from "./session-state"
+import { shouldSessionHoldWakeLock } from "./wake-lock-eligibility"
 
 function getSession(instanceId: string, sessionId: string): Session | null {
   const instanceSessions = sessions().get(instanceId)
   return instanceSessions?.get(sessionId) ?? null
 }
 
+export function hasWakeLockEligibleWork(instanceId: string): boolean {
+  const instanceSessions = sessions().get(instanceId)
+  if (!instanceSessions) {
+    return false
+  }
+
+  for (const session of instanceSessions.values()) {
+    if (shouldSessionHoldWakeLock(session)) {
+      return true
+    }
+  }
+
+  return false
+}
+
 export function getSessionStatus(instanceId: string, sessionId: string): SessionStatus {
   const session = getSession(instanceId, sessionId)
   if (!session) {