Well aware. I think it would be in everyone's interest that we reduce our dependence on China, and in the EU's interest in particular to try to reduce dependence on the US. And I'm saying this as an American.
It is definitely not a monopoly. A duopoly, sure. I'll add that if Android was as closed down as Apple is, I'd feel differently about the necessity of government regulations to address competition.
I don't think the government should make that determination - it should be up to the companies providing the OS. If they want to offer alternatives, great, if not, that's a decision that competitors can and should exploit. If every major OS prohibited alternative browsers, then government intervention might be warranted. And I certainly don't think that "browser choice screens" are a good idea.
I think the status quo for Apple was working fine, where those who wanted to use a different default browser had that ability, and those who didn't care stuck with the default, that is safe, secure, and private (particularly compared to the competition). The result of this regulation is that many "normal" users (the type who don't post on tech enthusiast forums like MacRumors) end up either 1) confused with where Safari went and why there's a different app 2) electing to use Chrome because it's the browser they've heard of.
Completely anecdotal but I just asked my mother-in-law if she knew the name of Apple's browser. She recognized the icon but didn't know the name. I suspect she'd choose Chrome if presented with a browser choice screen and didn't see the Safari icon. I also suspect she is not alone. So I strongly suspect what the EU has done here is actually the opposite of what they intended - further strengthening the market leader.