Does BIP 32 always implicitly assume secp256k1 elliptic curve cryptography (ECC) is to be applied, or can BIP 32 technology also be applied to create extended public or private keys that can readily be converted to say ed25519 private/public keypairs? One of the reasons I ask is because if a mathematical or computational backdoor is ever discovered for secp256k1, can ed25519 slide right in or does BIP 32 need to be re-engineered to support ed25519? Ed25519 can also be applied to provide Schnorr Signature capabilities.
Any Elliptic Curve could work in the BIP32 scheme. The only property of a Curve that BIP32 relies on is that a * G + b *G = (a + b mod N) * G, which is true for any Elliptic Curve.
Secp256k1 is a 'Koblitz' curve, which just means its choice of parameters enables very fast scalar multiplication (computing a multiple of the Generator point).
With that said, if a vulnerability was discovered in secp256k1, it's not like everyone could just switch over easily. That would require a major change to the Bitcoin consensus system, and require coordination of many software systems.