Which is the irreducible polynomial in GF(2^256) used in AES256-GCM?
The AES block cipher supports various key sizes of 128, 192, and 256 bits, and a single block size of 128 bits. The degree-8 polynomial $x^8+x^4+x^3+x+1$ is the one used in AES-{128,192,256} for MixColumn and SubBytes.

There is no $\operatorname{GF}(2^{256})$ in GCM because GCM only supports block size of 128 bits. The degree-128 polynomial $x^{128}+x^7+x^2+x+1$ is the one used in GCM.