chore: roll Playwright to 1.62.0

[Skn0tt]

Closes #3145

[Skn0tt]

The failing CI seems to be related to microsoft/playwright#41303 and page.close() hanging, i'm looking into it.

[Skn0tt]

5aee361 should fix it by moving our fixtures here closer to what upstream does, and relying on context.close() for cleanup solely instead of also having page.close() on page fixture teardown. This only affects this repo and not our customers, the playwright-pytest integration already has this behaviour.