While I tentatively agree with what you've said, I'll add that if someone breaks SHA-256 or SHA-512 anytime soon, all three.
No, breaking (by break I assume you mean a pre-image attack) SHA256 or SHA512 will not effect your private keys at all. SHA256 is not used in anything related to key derivation. SHA512 is used in key derivation, but you don't actually know the SHA512 hash unless you have a private key from the wallet, and even then, you only know half of the hash, not the full hash, so you can't find the preimage which would be the parent private key. These hash functions really are not involved in hardware wallets at all.
If someone breaks SHA-256 they'll be able to break SHA-512 in short order, relatively speaking. The orders of magnitude beyond what's being done right now say it's so. All avenues for modern cracking point to quantum state side channel attacks being the most likely candidates. Deriving a means of bypassing locks isn't what I'm referring to. And since hardware wallets rely on ECDSA for the most part (512 bits in some cases, re: BIP39), breaking SHA-256 definitely does have bearing. Standard cryptographic models aren't going allow it to be broken, but novel ones will. The fact that entropic quantum entanglement and the entanglement measure is an NP-Complete measurement means that no one's been able to look at it, except in novel effects-related efforts. I'm currently looking at electromigration as a candidate for bearing said data as it's related directly to quantum discord. Call it irrelevant if you like, but the security-level for bitcoin is based upon standard models, not taking into account measures that are outside of the boundaries. We've seen that bitcoin blocks can be falsely generated with the initial genesis block, and derive from there. Yes, that's a straw man for now, but that fact doesn't negate the weak foundations. Again, call that irrelevant or also un-prove-able. If I had a working model I'd be sitting in Maui. So, "pics or it didn't happen" all you want, I'll just leave this here so someday when it occurs I can refer back to it.