You already know how to fix a single flaky test. This lecture is about the situation you will inherit: a suite where forty tests fail at random and everyone has given up.
You cannot debug forty tests one by one. You need a different approach.
Step 1: measure before you fix anything. Playwright's HTML report and JSON reporter both record which tests were retried. Collect that over a week and count failures per test.
Do not skip this. Without numbers, "the suite is flaky" is a feeling, and you cannot show progress to a manager who is asking why testing takes so long.