Quantum resistant improvements wouldn't affect your private keys at all. It would only introduce new address formats. Same seed words, same key generation methods for new wallets, just new address formats.

That said, I do think there is a new standard way to create, backup and secure your private keys that may or may not come in the form of seed words and it will be the new recommended way to secure your bitcoin and be quite disruptive for those who want to stay current.

All upgrades in bitcoin are backwards compatible. No change will force users to change their backups or move their bitcoin to new addresses, but those who don't may find themselves in less secure or less easy to recover situations in the future.