How keys are stored: encrypted keystore files and seed phrases.
Why it matters: Quantum-safe, but only as strong as your password and how well you guard your seed.
On the map: validator keystores, wallet seeds
How keys rest on disk and on paper: validator keystores (EIP-2335)[1] and wallet seed phrases (BIP-39 and BIP-32)[2, 3].
These are mostly hash and symmetric cryptography, so they are quantum-resistant. The weak points are human: weak passwords, phished or leaked seed phrases, and bad randomness at generation time.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.