E2E Tests: Only install Chromium and its deps for Playwright

[tbradsha]

Right now we use default settings to install Chromium, Firefox, and Webkit for Playwright prior to running E2E tests, but we only use Chromium in our config. GH Actions also shows missing dependencies. This PR fixes both of those by switching from this:

playwright install

to this:

playwright install --with-deps chromium

It trades about 10 seconds of unneeded installs for about 15 seconds of dependencies, which means this is technically slower by a few seconds. We could remove the --with-deps if we prefer since tests run fine anyway, though I don't see a way to suppress those dependency warnings.

I considered --only-shell, but this would force headless on local installs, which isn't ideal.

Other information:

• Have you written new tests for your changes, if applicable?
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Jetpack product discussion

Does this pull request change what data or activity we track or use?

Testing instructions:

• Is CI happy?
• Is only Chromium (and FFMPEG) downloading)?
• Is the dependency warning gone?
• In particular, are E2E tests passing (as well as they did before)?

Here's an old run with multiple browsers downloaded and the dependency warning:
https://github.com/Automattic/jetpack/actions/runs/12585666388/job/35077965663

[github-actions]

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[github-actions]

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[robertsreberski]

That looks like a good optimization for me, thanks for implementing that!

It might be interesting to include the context of how did you figure out the issue.

[tbradsha]

It might be interesting to include the context of how did you figure out the issue.

In this case I saw the output in the GH Action logs downloading multiple browsers and showing the dependency error, knew we only used one browser, and so updated our process to download the one with its dependencies.