I had understood that Playwright actually used the DevTools protocol rather than the WebDriver protocol, as mentioned here:

https://github.com/microsoft/playwright/issues/4862

And there's a bit of detail about how they're different here:

https://stackoverflow.com/q/50939116/142780

However that's more a detail and doesn't really undermine your point about Firefox / Safari being handled differently, it's just that Playwright implemented their own versions of the protocol for those two non-Chromium based browsers