Aurora store is an excellent alternative client for the play store and does not require a google account. However, it downloads apps directly from google servers and if on one side it’s a good thing because you have the same security you would have using the play store on the other side you continue to depend on google.
In addition, aurora store goes against the play store’s terms of service, so if you use it with your google account you might be suspended (although I’ve never heard of this happening).
The best way to break away from google is to look for alternative apps on f-droid and try to use f-droid as your main store as much as possible and use aurora store only in case of indispensable and irreplaceable apps not available on f-droid.
Personally on my phone I’ve installed ~220 apps (many of them just to test them) and only 7 from aurora store (5 of which are open source anyway), all the others are installed from the official f-droid repository or from the izzyondroid repo.