why does it matter which way you do it, treating it as a string vs a number though?
SHA256 takes bytes as input. Each character from a dice rolls string takes 8 bits, whereas in a dice rolls number (integer with base 6), each character takes about 1.66 bits on average (1, 2, 3, 4 give 2 bits, while 5, 6 give 1 bit). Therefore, hashing a string would give you a false sense of security. For example, string "123456" is 6 bytes, but (123456)
6 is 6*1.66 = ~9.96 bits. which is about 1 byte.
To think it more simply, in a string, each character takes up to 2^8 = 256 different values (00000000, 00000001 [...], 11111110, 11111111), but a dice roll can only give up to 6 different values. Therefore, a 128-bit random number doesn't have the same security as a 128-bit string that is consisted of 16 dice rolled characters.