Browsers ask permission first. Also I don't see how having to install an app is any better other than being better for devs to track you.
I might install one app per hundred sites that annoyingly prompt for notification permissions, though.
And I install one app per hundred sites that annoyingly prompt me to install their app so they can give me push notifications (or, worse, a working website because they didn't bother even trying to build their product as a website anymore because of the lack of push notifications; it is ridiculous). So? The site is going to prompt me either way. This argument makes no sense: of course I would rather get promoted for the one feature I don't want to give them instead of an attempt to upsell me on an entirely different experience after being served crippled content... that is a total no brainer.