I don't think the TLS negotiation will become meaningfully slower, as there are multiple threads being pulled on for how to make post quantum happen here with minimal regression, instead it will likely become meaningfully more complex and only slightly slower, continuing a trend that has been ratcheting for quite some time now. ECH and modern certificate revocation checking schemes are also contributing to this.

The increase in complexity is a huge problem. It is arguably justifiable but simultaneously concerning. It's already quite hard to make a correct TLS implementation as it is.

(Personally though, I still like post quantum encryption. It's a nice hedge in case ECC and/or RSA do fall any time soon, whether by quantum computer or simply math.)