**feat(examples, core, docs): add flushStatistics example, implementation, and documentation**

- **Examples**: Added a new `flush-statistics-example.js` script to demonstrate the usage of the `flushStatistics` method for ensuring updated statistics after data insertion.
- **Core**:
  - Implemented `flushStatistics` in the `BrainyData` class to allow immediate flushing of statistics to storage.
  - Updated `BaseStorageAdapter` with `flushStatisticsToStorage` to support flushing cached statistics.
  - Modified the `shutDown` method to ensure statistics are flushed before database shutdown.
- **Documentation**: Added `statistics-flush-solution.md` to explain the batch update mechanism, the issue with delayed statistics updates, and how to manually flush statistics in storage.

**Purpose**: Provide users with the ability to manually flush statistics for real-time accuracy, particularly useful for systems relying on immediate updates. Improved documentation and examples to guide developers in implementing and using this functionality effectively.

src/storage/adapters/baseStorageAdapter.ts

@@ -290,6 +290,20 @@ export abstract class BaseStorageAdapter implements StorageAdapter {
     this.scheduleBatchUpdate()
   }
 
+  /**
+   * Force an immediate flush of statistics to storage
+   * This ensures that any pending statistics updates are written to persistent storage
+   */
+  async flushStatisticsToStorage(): Promise<void> {
+    // If there are no statistics in cache or they haven't been modified, nothing to flush
+    if (!this.statisticsCache || !this.statisticsModified) {
+      return
+    }
+
+    // Call the protected flushStatistics method to immediately write to storage
+    await this.flushStatistics()
+  }
+
   /**
    * Create default statistics data
    * @returns Default statistics data