Add Microsoft Playwright MCP server to README (#2678)

Author: mademan12

README.md

@@ -350,6 +350,7 @@ Official integrations are maintained by companies building production ready MCP
 - <img height="12" width="12" src="https://avatars.githubusercontent.com/u/54333248" /> **[Pinecone Assistant](https://github.com/pinecone-io/assistant-mcp)** - Retrieves context from your [Pinecone Assistant](https://docs.pinecone.io/guides/assistant/mcp-server) knowledge base.
 - <img height="12" width="12" src="https://pipedream.com/favicon.ico" alt="Pipedream Logo" /> **[Pipedream](https://github.com/PipedreamHQ/pipedream/tree/master/modelcontextprotocol)** - Connect with 2,500 APIs with 8,000+ prebuilt tools.
 - <img height="12" width="12" src="https://playcanvas.com/static-assets/images/icons/favicon.png" alt="PlayCanvas Logo" /> **[PlayCanvas](https://github.com/playcanvas/editor-mcp-server)** - Create interactive 3D web apps with the PlayCanvas Editor.
+- <img height="12" width="12" src="https://playwright.dev/img/playwright-logo.ico" alt="Playwright Logo" /> **[Playwright](https://github.com/microsoft/playwright-mcp)** — Browser automation MCP server using Playwright to run tests, navigate pages, capture screenshots, scrape content, and automate web interactions reliably.
 - <img height="12" width="12" src="https://www.plugged.in/favicon.ico" alt="Plugged.in Logo" /> **[Plugged.in](https://github.com/VeriTeknik/pluggedin-mcp)** - A comprehensive proxy that combines multiple MCP servers into a single MCP. It provides discovery and management of tools, prompts, resources, and templates across servers, plus a playground for debugging when building MCP servers.
 - <img height="12" width="12" src="https://github.com/port-labs/port-mcp-server/blob/main/assets/port_symbol_white.svg" alt="Port Logo" /> **[Port IO](https://github.com/port-labs/port-mcp-server)** - Access and manage your software catalog to improve service quality and compliance.
 - **[PostHog](https://github.com/posthog/mcp)** - Interact with PostHog analytics, feature flags, error tracking and more with the official PostHog MCP server.