feat: progressive init and readiness API for cloud storage

- Add `initMode` option to all cloud storage adapters (GCS, S3, Azure)
  - 'auto' (default): progressive in cloud, strict locally
  - 'progressive': <200ms cold starts, lazy bucket validation
  - 'strict': blocking validation (current behavior)

- Add cloud environment auto-detection for:
  - Cloud Run (K_SERVICE, K_REVISION)
  - AWS Lambda (AWS_LAMBDA_FUNCTION_NAME)
  - Cloud Functions (FUNCTIONS_TARGET)
  - Azure Functions (AZURE_FUNCTIONS_ENVIRONMENT)

- Add readiness API to Brainy class:
  - `brain.ready`: Promise that resolves when init() completes
  - `brain.isFullyInitialized()`: checks if background tasks done
  - `brain.awaitBackgroundInit()`: waits for background tasks

- Lazy bucket validation on first write (not during init)
- Background count synchronization
- Update AWS/GCP deployment docs with readiness patterns

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

docs/api/COMPREHENSIVE_API_OVERVIEW.md

@@ -20,6 +20,66 @@ const brain = new Brainy({
 await brain.init()
 ```
 
+## Readiness API (v7.3.0+)
+
+For reliable initialization detection, especially in cloud environments with progressive initialization:
+
+### `brain.ready` - Await Initialization
+
+```typescript
+const brain = new Brainy()
+brain.init()  // Fire and forget
+
+// Elsewhere (e.g., API handler)
+await brain.ready  // Wait until init() completes
+const results = await brain.find({ query: 'test' })
+```
+
+### `brain.isInitialized` - Check Basic Readiness
+
+```typescript
+if (brain.isInitialized) {
+  // Safe to use brain methods
+}
+```
+
+### `brain.isFullyInitialized()` - Check Background Tasks
+
+```typescript
+// Returns true when ALL initialization is complete, including background tasks
+// Useful for cloud storage adapters with progressive initialization
+if (brain.isFullyInitialized()) {
+  console.log('All background tasks complete')
+}
+```
+
+### `brain.awaitBackgroundInit()` - Wait for Background Tasks
+
+```typescript
+const brain = new Brainy({ storage: { type: 'gcs', ... } })
+await brain.init()  // Fast return in cloud (<200ms)
+
+// Optional: wait for all background tasks (bucket validation, count sync)
+await brain.awaitBackgroundInit()
+console.log('Fully initialized including background tasks')
+```
+
+### Health Check Pattern
+
+```typescript
+app.get('/health', async (req, res) => {
+  try {
+    await brain.ready
+    res.json({
+      status: 'ready',
+      fullyInitialized: brain.isFullyInitialized()
+    })
+  } catch (error) {
+    res.status(503).json({ status: 'initializing', error: error.message })
+  }
+})
+```
+
 ## Core CRUD Operations
 
 ### `brain.add(params)` - Add Entity