I've never had google ads randomly pop up on my desktop environment. When that starts happening, maybe you have a point.
Conversely, I don't use the start menu. At best I hit start and type the application I use. But on my Windows machine I mostly live inside my browser and Steam / game libraries, which are pinned to my start bar.
That isn't a fair comparison because each company primarily advertises from their monopoly position. Google does not have a monopoly position on platforms, only services. Microsoft is the opposite.
If you flip it around, Microsoft shows you one advert if you haven't turned them off entirely. Where as Google shows you an advert every time you visit every service they have and you can't turn it off.
Is your desktop environment Chrome OS?
Do you get Microsoft ads whenever you visit google.com from the Chrome Web Browser?