GrapheneOS actually recommends against using Aurora and instead just using the Play Store, so this shouldn't really hurt users. For extra privacy, you can sign into the Play Store with a Google Account that isn't tied to anything else.
Although the nice thing about Aurora Store is it allows you to install apps without a google account linked to your device, keeping Google Play Services signed-out. Somewhere in the FAQ GOS advertises that Play Services can be used without signing in, but they also recommend the official Play Store (which requires signing in) and explicitly don't recommend Aurora (which doesn't). Unless I'm missing something, I don't…
You still need to supply Play Services:
GrapheneOS uses Sandboxed Google Play. LineageOS requires flashing a package like MindTheGapps. There is also microG, an open-source reimplementation of Play Services APIs.