Considering how the asymmetric cryptography part of Ethereum is an exact copy of Bitcoin's, there is no difference between the private and public keys. The same elliptic curve and same algorithm is used to generate them.
Keep in mind that it is never a good idea to use altcoin related tools or wallets to generate a key used for bitcoin. Your funds will be at risk.
this solution didn't result in the correct Taproot address.
Why do you think it is not the "correct" address? What are you comparing it with?
There are two different ways to generate a Taproot address from the same key and both will be "correct".