Big O analysis never implies size in bits. It's just often done. In this case, n is just the numerical value of the input, so I don't think this is correct.
https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality...
As you'll see they are using the number of digits, not the value of the number, because the number of digits is the size of the input.
You can find countless examples of this in literature. So this is not a 'personally-interesting' way as you assert.