Before you write anything, you need one picture in your head. Everything else in Playwright follows from it, and people who skip this spend weeks confused about missing await keywords.
A Playwright test is a Node.js program that remote-controls a real browser. Your code runs in one process. Chrome (or Firefox, or WebKit) runs in another. Playwright sends it commands and waits for answers.
That one fact explains the thing you will type most: await.