How many bytes of data does AES 256 encrypt at one time?
AES has always 128-bit block size with 128,192 and 256-bit keyspaces.  Therefore, you can encrypt 16-byte at a time if you are using ECB and CBC modes. By using CTR mode you can encrypt 1-bit to 128-bit.

Some people confuse AES with Rijndael where AES is a variant of the Rijndael. Some old libraries use the Rijndael (see RijndaelManaged). Rijndael can have 128, 160, 192, 224, and 256-bit block size. Note that these are not standardized, see FIPS 197.