feat: native sync state (#14190)

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

## Summary by CodeRabbit

* **New Features**
* Added indexed clock management capabilities for documents, enabling
get, set, and clear operations across Android, iOS, Electron, and web
platforms.

* **Refactor**
* Improved storage architecture to dynamically select platform-specific
implementations (SQLite for Electron, IndexedDB for others).

* **Bug Fixes**
* Enhanced document operations to properly maintain and clean up indexer
synchronization state during document lifecycle changes.

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settings.</sub>

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

packages/common/nbstore/src/impls/sqlite/indexer-sync.ts

@@ -0,0 +1,38 @@
+import { share } from '../../connection';
+import {
+  type DocIndexedClock,
+  IndexerSyncStorageBase,
+} from '../../storage/indexer-sync';
+import { NativeDBConnection, type SqliteNativeDBOptions } from './db';
+
+export class SqliteIndexerSyncStorage extends IndexerSyncStorageBase {
+  static readonly identifier = 'SqliteIndexerSyncStorage';
+
+  override connection = share(new NativeDBConnection(this.options));
+
+  constructor(private readonly options: SqliteNativeDBOptions) {
+    super();
+  }
+
+  private get db() {
+    return this.connection.apis;
+  }
+
+  override async getDocIndexedClock(
+    docId: string
+  ): Promise<DocIndexedClock | null> {
+    return this.db.getDocIndexedClock(docId);
+  }
+
+  override async setDocIndexedClock(clock: DocIndexedClock): Promise<void> {
+    await this.db.setDocIndexedClock(
+      clock.docId,
+      clock.timestamp,
+      clock.indexerVersion
+    );
+  }
+
+  override async clearDocIndexedClock(docId: string): Promise<void> {
+    await this.db.clearDocIndexedClock(docId);
+  }
+}