Used to be you'd look at your server logs and see referrer headers of google.com/?q=search+terms
Then they broke that (deliberately, well before cross origin header concerns were a thing) so you'd have to sign up for their webmaster tools.
Google also did 100% make search worse on purpose as this great piece discusses: https://www.wheresyoured.at/the-men-who-killed-google/
Doctorow goes into greater detail on how Google purposely worsened Google search in his book Enshittification. It’s a very thorough chapter and it’s clear what they did. They were chasing “engagement hacks.”