test: add playwright testing to start-basic

[jasonLaster]

This adds some playwright tests to start-basic to ensure that it's working correctly.

• pnpm run test:playwright runs the tests locally
• pnpm run test:playwright:replay runs the tests with the Replay browser

To view the replays, join the TanStack router team. Here's an example replay of one of the new tests.

https://www.loom.com/share/d31ef881d2894cdd9e566e56ce9a223d