I take your point that it isn't literally modifying the html of the web page—but if it was, wouldn't the result look exactly like this? Visually, the banner does not look like a part of the browser chrome, Microsoft put it in the web page's space. That area belongs to the website, browsers aren't supposed to mess with it!
What Microsoft has done here is certainly an escalation of what Google had been doing in recent years. Perhaps Google shouldn't have started being so aggressive with the popups to begin with.
I don't think it's that different. Google has a pop up ad when using Gmail that asks you to "upgrade" to Chrome. Both are leveraging a near monopoly in something else to hard sell users on their browser.
