There are other Android stores. Amazon ran one for the longest time. Many brands have their own app stores as well.

It's the app publishers defaulting to Google that's the biggest issue.

At least WhatsApp has an official APK download, most apps don't.

That said, Google will still let you update apps without being signed in. Hold the Play Store icon to open the quick action menu. From there you can go to "my apps" and update all of the apps on your phone, bypassing the login prompt. Not great, but a workaround that should do the trick while Aurora finds another way to hack their way into the Play Store APIs.