it collects call logs, contacts, location, your microphone, and much more

From my cursory look at the APK this looks to be complete misinformation. The app has no permissions beside accessing the Internet and reading some basic device status information. It is not a system app either, so it cannot elevate its privileges beyond that. Therefore it can already do less than most other Google apps you have on your phone.

There’s one main service that’s exposed: the ClassificationApiService. Further, a machine learning library included - most likely for local/offline inference. And that all makes sense if you read what Google has to say about the app:

Sensitive Content Warnings is an optional feature that blurs images that may contain nudity before viewing, and then prompts with a “speed bump” that contains help-finding resources and options, including to view the content. When the feature is enabled, and an image that may contain nudity is about to be sent or forwarded, it also provides a speed bump to remind users of the risks of sending nude imagery and preventing accidental shares.

Now all that said, Google should definitely communicate the intent of these applications better, and not silently install some suspicious looking app without consent. But if Google wanted more data from you - most of the time they can just ask you to share it - Where do you store your contacts? How do you share files with your other devices?

In any case I do think that this sort of client side scanning is still concerning, since it’s now just one step away from forwarding images that trigger the classification service to law enforcement.