No. "Post-quantum" is not a kind of cryptography; it's an attribute of many different kinds of cryptography. SIKE and modular lattices are completely unrelated. SIKE is moon math that genuinely was introduced to mainstream cryptographers as a post-quantum construction. Lattices have been carefully studied for decades; in the 1990s, it was a live discussion whether the successor to RSA was going to be elliptic curves or lattices.

People bring up SIKE/SIDH in these discussions because Daniel Bernstein has used it as innuendo in his arguments against the MLKEM standard (always left out of those discussions: Bernstein himself backed a lattice KEM in the same competition). It's aggravating because its very clear that he's succeeded in getting people to believe that SIDH somehow reflects on lattice cryptography. That's not a problem because it's persuasive (no cryptographer would take that argument seriously) but rather because he's succeeded in making people say dumb things.

Worth mentioning the lattice KEM he backed (NTRU prime) is part of a class of lattice-based assumptions that admitted devastating attacks (though not in the parameter regime relevant to public-key cryptography applications). By this I mean the dense sub lattice attacks on NTRU.

He has also repeatedly pointed to (seemingly random) pieces of lattice cryptography and claimed that it is the cause for concern/plausibly where attacks may come from. Here, I mean the galois group structure, the whole “quotient vs product” stuff he was doing trying to pretend LWE is a variant of ntru (and less secure, which was explicitly wrong), and his “spherical models” claims. These last ones included an explicit claim of subexponential attacks to be presented later, which have been delayed for a number of years now.

In short, his fearmongering over lattices, while persistent, has never been right. He’s pointed fingers at things we have not found issues with, and either backed sides in debates which ended up being less secure (NTRU vs LWE), or completely missed other things (say the sPIP attacks a decade ago). He may plausibly be the least credible person to make predictions about lattices in the world.

This is ignoring all of his other explicitly embarrassing behavior, for example

1. Insinuating all lattice cryptographers are on the payroll of the NSA. The winning schemes were European teams predominantly.

2. Adding a license to all emails he sends in the IETF wg that is incompatible with the wg. This ends up with him getting censure, which he then argues is unjust.

3. Recently, finding a bug in a 2017 piece of software, and then fabricating 3 other bugs. He then wrote a 60 page paper on it, using it as justification to argue against lattices. All of the bugs would be caught by standard high quality testing procedures, eg mutation testing, which he appears unfamiliar with. I believe the “actual” bug (from the v1 reference impl a decade ago) is caught by current test vectors as well.