Well, yes, because it's Google's website.

It would be quite different if Google's browser started modifying Microsoft's websites, as Microsoft is Google's.

It is not modifying the website. It is microsofts browser that shows you stuff above the website....

I think both are absolutely disgusting

I take your point that it isn't literally modifying the html of the web page--but if it was, wouldn't it look exactly like this? It does not visually look like a part of the browser chrome, it's in the webpage's space. Browsers aren't supposed to mess with that!

Wonder where that banner shows up in the DOM, in the dev tools console... ?

To be clear, I suspect it doesn't show up in dev tools, presumably it's rendered as part of the browser UI. But visually it doesn't look that way!

They absolutely DO mess with it if you have an ad-blocker installed on your browser.

Of course, the user explicitly installed the ad-blocker; the user didn't expect MS Edge to screw with the way the web page looks.

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.

Yes, I think both are absolutely disgusting too.

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.