[Bug]: When CLI was installed along with 1.62, newly installed skills still reference `playwright-cli` instead of `npx playwright cli`

Version

1.62

Steps to reproduce

1. npm init playwright@latest (without installing browsers)
2. npx playwright install chromium
3. npx playwright cli install --skills agents

In GitHub Copilot in vscode enter a prompt similar to
Using the playwright-cli skills, open a new (headful) browser, navigate to https://www.playwright.dev

Expected behavior

I expected the browser to open and navigate to the Playwright website.

Actual behavior

It's trying to execute playwright-cli and not finding it, because it's only installed as playwright cli

Additional context

No response

Environment

System:
    OS: Windows 11 10.0.22631
    CPU: (16) x64 11th Gen Intel(R) Core(TM) i7-11850H @ 2.50GHz
    Memory: 40.71 GB / 63.67 GB
  Binaries:
    Node: 21.0.0 - C:\Program Files\nodejs\node.EXE
    npm: 10.2.0 - C:\Program Files\nodejs\npm.CMD
  IDEs:
    VSCode: 1.128.0 - C:\Users\Eric.Veltman\AppData\Local\Programs\Microsoft VS Code\bin\code.CMD
  Languages:
    Bash: 5.1.16 - C:\WINDOWS\system32\bash.EXE
  npmPackages:
    @playwright/test: ^1.62.1 => 1.62.1