Private keys are not stored, They are deterministically generated of the seed data.
The seed encodes up to 256 bits of random entropy in a human readable form with a verification sum attached. These details are summarized in BIP39
This entropy is passed through the PBKDF2 hash function to produce a master private key and a chaining key, which are used to generate more private keys with HKDF-SHA512. These details are described in BIP32 – Hierarchical deterministic portfolios.
When you enter your seed phrase in a software that supports these two BIPs, the software will cache the private keys it generates locally, since recreating them every time the software is run would be costly and inefficient.