Is AES-256 a post-quantum secure cipher or not? We know Grover's algorithm speedup brute-force attacks two times faster in block ciphers (e.g brute-forcing 128-bit keys take $2^{64}$ operations, not $2^{128}$).
That explains why we are using 256-bit keys to encrypt top secrets. But latest practical attack on AES shows brute-forcing AES-256 take $2^{100}$ operations.
Does this attack work with Grover's search to make AES cipher quantum unresistant?
Biclique cryptanalysis is the current best-known attack on AES. It reduces the security of AES-256 from $2^{256}$ to $2^{254.4}$. Related key attacks are not practical attacks, as they should never occur in the wild. They are symptomatic of poor implementation and contrary to the recommended use of AES.

The best known theoretical attack is Grover's quantum search algorithm. As you pointed out, this allows us to search an unsorted database of $n$ entries in $\sqrt{n}$ operations. As such, AES-256 is secure for a medium-term against a quantum attack, however, AES-128 can be broken, and AES-192 isn't looking that good.

With the advances in computational power (doubling every 18 months), and the development of quantum computers, no set keysize is safe indefinitely. The use of Grover is just one of the gigantic leaps.

I would still class AES as quantum resistant, so long as the best-known attack is still some form of an exhaustive search of the keyspace.

As for your question about using different attacks: Combining attacks rarely works as you need all of your attacks to reveal exclusive bits of the key. Given that the best attack on AES doesn't even reveal 2, you will be hard pushed to make a reasonable attack like this.