fix(playwright): use npm run to start the server on default port

[zetaraku]

Description

When running Playwright end-to-end testing from Playwright Test for VSCode, an error is thrown:

Error: Process from config.webServer was not able to start. Exit code: 1

This is probably because the extension runs without adding node_modules/.bin to PATH like npm run does.

What this PR does

This PR uses npm run to start the server and adjusts the port according to the default port of vite dev or vite preview.

[cexbrayat]

LGTM, thanks for the PR!