One last post then it's time for the weekend.
A good way to think about 8130 is to go back to pre-AA Ethereum.
A secp256k1 key controlled an account, and that mapping was an intrinsic, unchangeable property of the address.
EIP-8130 simply makes that mapping updatable, to any contract defined authentication scheme and you update those with a signed payload, similar to a transaction. Those mappings need to live somewhere and thats the keystore.
ERC-4337 + ERC-1271 went a different direction, fusing authentication and authorization in one codebase per implementation.
8130 shares a lot of DNA with 7702. Authorization is external to wallet bytecode, execution code lives in the account address(batch calls etc), but now that external authorization can be managed!