This commit makes the following required changes:
- Replace custom cache trimming logic in favor of the (per our request)
newly added `trimCache` method in Puppeteer. Not only does this greatly
simplify our code and prevents having to import Puppeteer internals,
it's also necessary because Puppeteer 20 removed the `BrowserFetcher`
API in favor of the new separate `@puppeteer/browsers` package.
- Start browsers in series instead of in parallel. Parallel browser
starts broke since Puppetter 19.1.0 and it turns out that it has never
been supported officially, so it worked more-or-less by accident.
Starting browsers in series is the supported way, is almost equally
fast and ensures that we avoid any race conditions during startup.
Finally, it also allows us to remove the `browserPromise` state on our
session objects.
Fixes#15865.