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But Google says its service is simply the most popular.

"We have submitted evidence showing that the most common search query on Bing is, by far, 'Google'"

I assume they have collected this evidence from Chrome users?

0 Chrome users use Bing (rounded down)

Probably not, I imagine the vast majority of this would be from Edge for Windows users.

How would they get that data?

Referrals

To google.com? Sure, but what about non-google-related searches on Bing?