Except they actually don't in this case. You're free to release a browser with any engine you choose on Android and distribute it through the Play Store.
My takeaway from that article is they don't, and haven't.
The splash screen for installing a package not from the play store is there to protect the end user. Without it there would probably be a much worse unwanted software issue on android.
I've been "side loading" or just "installing" applications on my android devices since the nexus one, without the help of the play store.
That’s not what the lawsuit is about. Google made backdoor deals to pay developers to release on the play store instead of their own 3rd party app store. They were found at fault for anti-competitive behavior.
They don't. They discourage it on the consumer end, but that also has good safety reasons behind it. They go a little too far in pushing people to Play Store over other app stores, and require basically any phone with Google Services to have Play Store, but that's a different matter.
They've never tried to dictate rules on what sideloaders, both on the supplier and consumer side, can and can't do like Apple has.
The closest they've ever done to this is use Play Protect against apps like Lucky Patcher. And that's a piracy app that, among other things, patches other applications to do things like bypass Google's payment systems and disable ads.
Thats absolutely correct, around android 6, it got real annoying to install 3rd party apps, settings called it somthing like "install apps from places other than the google play store".
Later, it got more restrictive, ironically, making it a real security feature.