Hi there,
I just encountered the same issues you did, also trying to switch from Play Store WhatsApp to getting it with Obtainium and using it without the Play Store.
The issue here is that Meta releases both apks with the same app ID com.whatsapp but different signatures. You can observe this if you download the apk directly from the website and open it with AppVerifier: the signature doesn't match the one in the AppVerifier database.
If I had to guess, the Play Store is failing to install WhatsApp because the OS still has the signature corresponding to the direct-download apk. I'd guess this is because the app is still installed in a different profile. You should be able to go into the owner profile and uninstall the app for all profiles.
As for the backup restore issue, I encountered the same error. In my case I am trying to transfer chat history from one phone to another, and so I also tried the chat transfer tool within WhatsApp, which failed with a similar error. I'm guessing in both cases this is a limitation of the backup functionality in WhatsApp, and not something that can be fixed.