feat(core): bettery save mode (#12996)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **New Features**
* Introduced a battery save mode that can pause background sync and
processing to conserve energy.
* Battery save mode is automatically enabled when the app window loses
focus and disabled when the window regains focus or is interacted with.
  * Available in both web and desktop (Electron) versions.

* **Improvements**
* Added user activity detection to optimize background operations for
better battery efficiency.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

packages/common/nbstore/src/sync/indexer/index.ts

@@ -159,6 +159,14 @@ export class IndexerSyncImpl implements IndexerSync {
     this.remote = Object.values(this.peers.remotes).find(remote => !!remote);
   }
 
+  enableBatterySaveMode() {
+    this.status.enableBatterySaveMode();
+  }
+
+  disableBatterySaveMode() {
+    this.status.disableBatterySaveMode();
+  }
+
   start() {
     if (this.abort) {
       this.abort.abort(MANUALLY_STOP);
@@ -611,6 +619,10 @@ class IndexerSyncStatus {
   currentJob: string | null = null;
   errorMessage: string | null = null;
   statusUpdatedSubject$ = new Subject<string | true>();
+  batterySaveMode: {
+    promise: Promise<void>;
+    resolve: () => void;
+  } | null = null;
 
   state$ = new Observable<IndexerSyncState>(subscribe => {
     const next = () => {
@@ -685,6 +697,9 @@ class IndexerSyncStatus {
   }
 
   async acceptJob(abort?: AbortSignal) {
+    if (this.batterySaveMode) {
+      await this.batterySaveMode.promise;
+    }
     const job = await this.jobs.asyncPop(abort);
     this.currentJob = job;
     this.statusUpdatedSubject$.next(job);
@@ -709,6 +724,18 @@ class IndexerSyncStatus {
     };
   }
 
+  enableBatterySaveMode() {
+    if (this.batterySaveMode) {
+      return;
+    }
+    this.batterySaveMode = Promise.withResolvers();
+  }
+
+  disableBatterySaveMode() {
+    this.batterySaveMode?.resolve();
+    this.batterySaveMode = null;
+  }
+
   reset() {
     // reset all state, except prioritySettings
     this.isReadonly = false;