The original AES-NI (which were SSE instructions) and also their initial correspondent in AVX performed 128-bit operations.
Later, 256-bit AES instructions were introduced, but significantly later than AVX2. Such 256-bit AES instructions, which double the AES throughput, are available in more recent CPUs, like AMD Zen 3 and Intel Alder Lake (the so-called VAES instructions).
Some of the more recent CPUs with AVX-512 support have added 512-bit AES instructions, for an extra doubling of the AES throughput.
Zen 5 (desktop and server) doubles the AES throughput in comparison with Zen 4, similarly with the double throughput for other vector operations.
In conclusion, on x86 CPUs there are many alternatives for AES, which have different throughputs: 128-bit SSE instructions since Westmere, 128-bit AVX instructions since Sandy Bridge, 256-bit VAES AVX instructions since Zen 3 and Alder Lake and 512-bit AVX-512 instructions since Ice Lake, but only in the CPUs with AVX-512 support.