DJB's narrative is a little selective here: Cloudflare has done some incredibly impressive things with post-quantum key agreement, which is arguably the "easy"[1] part of moving the Web PKI/TLS to a PQ setting. But key agreement doesn't tell the parties why they should trust each other; you need signatures and certificates for that, and those will need to be PQ-ready too.
That part is much harder, for both technical (larger certificates implied by most PQ signing schemes are much harder to reliably convey over packet networks) and political (the X.509 ecosystem moves very slowly, and penetration of new signature schemes takes years) reasons.
[1]: Nothing about it is easy.
Last I heard we were 1-2 orders of magnitude away from the error correction break even point for noise performance; that point where it would take an infinite number of noisy qubits to break 2048 bit RSA. So does this mean that we are still at an error rate of something like 10%?