Do any NIST PQC have "homomorphic" public keys, in the sense that any two pubkeys derive a combination pubkey?
No, this does not survive as is in the quantum world, since all discrete logarithm schemes (including Diffie-Hellman) are broken.

And more generally, this is probably not possible in the quantum world a priori, because it would imply having group homomorphic properties, which are hindered by the fact that Shor's algorithm is actually made of two parts:


A reduction of the factoring problem to the problem of order-finding.
A quantum algorithm to solve the order-finding problem


and the problem is that the order finding part implies that it allows to find the order of a group element, thus allowing to break the discrete logarithm easily.

There is even an impossibility result from 2014 for group homomorphic encryption in the quantum world.
Its core idea is basically that you can win the IND-CPA game by choosing two messages $m_0$ and $m_1$ such that $m_0=e$, and $m_1\neq e$, for $e$ the identity element in your plaintext group, which will be mapped when encrypted to the identity element of the ciphertext group, and since you can compute the order of an element using Shor's order finding part, you can find whether the ciphertext has order 1 (in which cases it corresponds to $m_0$) or not.
And the same kind of problems will arise with digital signatures or key exchanges algorithms.

This is also the reason why it is extremely difficult to come up with zero-knowledge proofs that are quantum safe.