Except edge then opens and presents you with some message about setting it to the default browser (which a lot of people will just click ok to make it go away)
That an internal OS system (help) opens in the OS browser I'm willing to accept. That every browser says "please please make us the default browser" is annoying but hardly unique for Edge.
This is just the combination of the two.
I don't think enough people use Win+Type+Enter queries, nor F1 help in Windows to make the discussion very interesting compared to the really interesting ones like which browsers will open a hyperlink in a non-browser app.
Edge is the only browser that periodically captures you in a full screen multiple pages nag screen when it's not default. It's also the only browser able to set itself as default without further interaction.
It does that when it's the default, too. I only occasionally use Windows, so couldn't be bothered to install something else. Yet, I feel that every other time I start it, I'm presented with some "use edge! it's so cool!" screen I have to sit through. It also insists on changing the search engine to bing. I'm usually pretty cautious and try not to press "ok" just so it leaves me alone, yet it managed to change it. For my needs, pretty much every search engine is good enough. I prefer google since I can convince it to use dark mode and use English instead of my local language (even though windows is set to use English as its display language).
Because I accept both things on their own, and I accept that the combination of them follows naturally. Then I must (reluctantly) accept unfortunate outcome of the combination.
I wouldn't say it's reasonable that browsers could never suggest they be made default, and I don't think it's reasonable that you can't have some OS function that wants to show e.g. a help section use the OS embedded browser.
That might be acceptable if no thought went into the combination of the two things.
I accept people must work at height. I accept that people occasionally fall over by accident. We have guard rails and harnesses so that I don't have to accept people falling to their death every time they trip at height.
For example it wouldn't be ridiculous to think that if the browser is tightly coupled with the OS (to the point that it doesn't change when you set the default browser) that you can have the embedded browser opened with a no nag/no ad flag set.
Just because its 2 things you'd otherwise accept doesn't mean it isn't a dark pattern. Lots of dark patterns (like the setting up of privacy / data sharing settings on google) do similar things.
