Eartho sounds like a something a user wants. We have found that privacy is an added bonus, but that it is only one of many features a developer wants.

Adding yet another button that users don't understand confuses users.

I'm the founder of Hellō and we have a similar service that has cooperative governance. https://hello.coop/

FWIW it is a myth that Google uses where you login with Google for retargeting. Big Tech is always concerned about having to share user specific usage with US agencies. Google considers knowing where you login to be toxic data that they want to dump as quickly as possible. There are more than enough other signals from re-targetting.