You can hate Google nagging you all you want, but they are doing it on their own properties. There is a cost/benefit calculation for them.
But if you inject ads into someone else's space and no one seems to care (or just blames Google) then the cost/benefit calculation changes completely and this could get quite ugly.
If in Google's product they can nag me every time I ask them to open a competitor's product, why shouldn't Microsoft's product nag me every time I ask them to open a competitor's product?
They're both shit from my perspective as a user, of course. But Microsoft is just using the Google playbook here.
As far as I know, Google don’t push Chrome on websites that aren’t theirs.
If you were watching a movie on Prime and Amazon inserted an ad before the movie that would be annoying but normal.
But what if your TV manufacturer injected an ad over the movie?
That would not be the moral equivalent of the first example, and if you just blamed Amazon then all the TV manufacturers would jump on the bandwagon.