E2e tests: merge Puppeteer into single job, split Playwright further

[ellatrix]

What?

The Playwright tests have been taking longer and longer (~20 mins), so it'd be good to add more jobs. Since there's still Puppeteer tests remaining, and other tests being added, this will only get worse over time, so I doubled the jobs.

Additionally, since the number of Puppeteer tests is greatly reduced, these test take barely any time anymore, so we can merge them all into one job I think. Again, over time, no tests should be left here.

Why?

How?

Testing Instructions

Testing Instructions for Keyboard

Screenshots or screencast

[Mamaduka]

I think we should also update the repo settings for required jobs. cc @talldan

[github-actions]

Flaky tests detected in 3160965.
Some tests passed with failed attempts. The failures may not be related to this commit but are still reported for visibility. See the documentation for more information.

🔍 Workflow run URL: https://github.com/WordPress/gutenberg/actions/runs/6945548945
📝 Reported issues:

• [Flaky Test] should move to the start of the first line on ArrowUp (-firefox) #56087 in /test/e2e/specs/editor/various/writing-flow.spec.js

[talldan]

I think we should also update the repo settings for required jobs. cc @talldan

Unfortunately that can only be done after the PR has merged and the new jobs have successfully completed once on trunk.

At least that's how it was the last few times.

[talldan]

I'll go ahead and merge this, then update the required checks 👍

[ellatrix]

Thanks!