fix #1563 (cdp): resolve page leaks and race conditions in concurrent crawling

Fix memory leaks and race conditions when using arun_many() with managed CDP browsers. Each crawl now gets proper page isolation with automatic cleanup while maintaining shared browser context.

Key fixes:
- Close non-session pages after crawling to prevent tab accumulation
- Add thread-safe page creation with locks to avoid concurrent access
- Improve page lifecycle management for managed vs non-managed browsers
- Keep session pages alive for authentication persistence
- Prevent TOCTOU (time-of-check-time-of-use) race conditions

This ensures stable parallel crawling without memory growth or browser instability.

tests/test_arun_many_cdp.py

@@ -0,0 +1,63 @@
+"""
+Test for arun_many with managed CDP browser to ensure each crawl gets its own tab.
+"""
+import pytest
+import asyncio
+from crawl4ai import AsyncWebCrawler, BrowserConfig, CrawlerRunConfig, CacheMode
+
+
+@pytest.mark.asyncio
+async def test_arun_many_with_cdp():
+    """Test arun_many opens a new tab for each url with managed CDP browser."""
+    # NOTE: Requires a running CDP browser at localhost:9222
+    # Can be started with: crwl cdp -d 9222
+    browser_cfg = BrowserConfig(
+        browser_type="cdp",
+        cdp_url="http://localhost:9222",
+        verbose=False,
+    )
+    urls = [
+        "https://example.com",
+        "https://httpbin.org/html",
+        "https://www.python.org",
+    ]
+    crawler_cfg = CrawlerRunConfig(
+        cache_mode=CacheMode.BYPASS,
+    )
+    async with AsyncWebCrawler(config=browser_cfg) as crawler:
+        results = await crawler.arun_many(urls=urls, config=crawler_cfg)
+        # All results should be successful and distinct
+        assert len(results) == 3
+        for result in results:
+            assert result.success, f"Crawl failed: {result.url} - {result.error_message}"
+            assert result.markdown is not None
+
+
+@pytest.mark.asyncio
+async def test_arun_many_with_cdp_sequential():
+    """Test arun_many sequentially to isolate issues."""
+    browser_cfg = BrowserConfig(
+        browser_type="cdp",
+        cdp_url="http://localhost:9222",
+        verbose=True,
+    )
+    urls = [
+        "https://example.com",
+        "https://httpbin.org/html", 
+        "https://www.python.org",
+    ]
+    crawler_cfg = CrawlerRunConfig(
+        cache_mode=CacheMode.BYPASS,
+    )
+    async with AsyncWebCrawler(config=browser_cfg) as crawler:
+        results = []
+        for url in urls:
+            result = await crawler.arun(url=url, config=crawler_cfg)
+            results.append(result)
+            assert result.success, f"Crawl failed: {result.url} - {result.error_message}"
+            assert result.markdown is not None
+        assert len(results) == 3
+
+
+if __name__ == "__main__":
+    asyncio.run(test_arun_many_with_cdp())