Your question is quite confusing, first of all you don’t add seed phrase to private key. Infact you get your private key from seed phrase and subsequently public key from private key. So having your seed phrase alone is ok.
If i start a new wallet and use the seed phrase i have instead, can i make it bech32?
Yes you can actually generate a native SegWit address or any type of address from your seed phrase by just clicking on the option when importing your seed phrase if it is Bip 39 click it and then the next option choose native SegWit as derivation path or any of the type you wish