Something that makes your end-to-end tests a heck of a lot more resilient is mocking your API so you're not hitting the network, and so your API responses are deterministic. Doing that also makes the tests run a lot faster. MSW is my preferred library for doing that, and there's a Playwright integration (https://www.npmjs.com/package/playwright-msw).

Mocking the API makes it really easy to response with failures too - having a test that checks the app handles a 500 error or a 401 Unauthorized is really useful, and a total pain to do without mocks.

You can test the API is working and returning what you'd expect with a different set of tests. :)