Why is my segwit private key generating a 3 address vs a bc1 address like how I originally generated?
There is no standard for specifying whether a private key should correspond to a bech32 address, P2SH nested segwit address, or P2PKH address (1... address). The WIF format has traditionally been used for P2PKH addresses. However some wallets now will decide to instead create a P2SH nested segwit address or even a bech32 address instead. But because there is no standard for private keys that correspond to segwit addresses, it is entirely up to the wallet to determine what kind of address to give you for a private key.

In your case, the wallet gave you a P2SH nested segwit address. But it could have just as easily given you the P2PKH address or the bech32 address since the private key can be used to produce all 3 types of addresses.