Fix local browser automation execution

[Jiahui-Gu]

Summary

• provide a local-only session isolation identity so documented localhost requests do not fail without platform headers
• invoke the npm Playwright CLI through its JavaScript entry point on Windows without introducing a shell
• document the Responses approval continuation required before browser tools run

Verification

• built the C# project with no warnings or errors
• started the repaired branch on a fresh local process and port
• received HTTP 200 readiness and a completed Responses invocation that called the browser tools and reported the Example Domain page title