Partially. I'm not familiar with the topic enough to explain everything exactly. But I want to warn you that using Aurora Store signed in may and likely will get your Google account banned and all your purchases gone

As the other commenter said, do not sign into Aurora store using your Google account because it will be banned. All of them are eventually. Do not take that risk with your personal account.

If you want to use proprietary apps the best option is probably dumping the APK from your "Googled" phone then sideloading it onto the new phone. However it may be difficult to keep up with updates unless you have a dedicated phone to download them.

Any app purchased from the Google Play Store needs to be downloaded and updated from the same in order for the paid functionality to work. Alternatively, download it cracked from somewhere else and risk potentially getting an infected app.

Those purchases will be lost if you want to degoogle. Just went through this some time ago and actually it was a good opportunity to think about which one I'm really using. The ones I really like and there was an opportunity to buy them outside of the Google ecosystem, I rebought (for example Tasker). For all others, I found good replacements.