A threat that's future, applied to data that's present
Post-quantum cryptography describes algorithms designed to remain secure even against an adversary with access to a sufficiently powerful quantum computer, capable of breaking several of the mathematical problems today's widely deployed cryptography relies on. No such computer exists at that capability today, but the migration matters now for a specific reason sometimes called 'harvest now, decrypt later': data encrypted today, if intercepted and stored, could potentially be decrypted retroactively once a capable quantum computer eventually exists, which makes today's encryption choices consequential for any data that needs to stay confidential well into the future.
For authorization specifically, this matters wherever long-term key material or credentials are involved — a certificate or key expected to remain valid and trusted for years is exactly the kind of thing worth reconsidering under this threat model now, well before the underlying algorithms are actually broken.
Whether the migration is feasible depends on a decision made years earlier
Crypto agility — a system's ability to swap out its underlying cryptographic algorithms without a fundamental redesign — is what determines whether this migration is a manageable, incremental undertaking or an enormous one. A crypto-agile system can adopt new algorithms as they mature and become standardized, well ahead of any actual quantum threat becoming practical; a system that hardcoded assumptions about a specific algorithm throughout has to defer the question until it becomes genuinely urgent, at which point the work is both harder and more time-pressured than it would have been if planned for in advance.