The simplified answer is, larger keys that demand a far larger effort to break, in a way similar to RSA-4096 vs RSA-2048.

The predicted timelines for quantum computer advances (and the requirements for practical applications) have shrunk dramatically in the past 15 years. What used to be a no-later-than-2035 recommendation for getting off e.g. RSA-2048 in good time, is today no-later-than-2030. The admission of 256-bit curves for ECDSA/ECDH has been supplanted by 384-bit curves already years ago.

In the absolutely ground shaking event that a future application of quantum computation somehow manages to cut Ed448's equivalent security of ~224 bits in half, exploring even a small portion of a 112-bit space will still cost more electrical energy than we can possibly provide.

The whole point is that RSA and ECDH can't be made safe against quantum computers by making the keys bigger. The speedup is exponential and so breaking a 4096-bit key is only twice as hard as a 2048-bit key. The 'cutting in keysize in half' is true in principle in general (but not in practice, as the article points out), but for some algorithms it's much worse.