Project Euler Solution 16: Power digit sum

Problem 16: Power digit sum of the Project Euler series is a bit disappointing.

$2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$.

What is the sum of the digits of the number $2^{1000}$?

This is very easy to do in Python with the arbitrary large integers:

def solution_direct() -> int:
    digits = [int(char) for char in str(2**1000)]
    return sum(digits)

And that takes just 41 µs to produce the correct answer. So it is clearly fast enough.

I thought that there must be a more clever way. In the forums (which one can access after having the correct solution) there are only answers of that kind. I had hoped that there was some more clever way. All contestants used some sort of big number library. So it maybe the only way to do this. I don't know enough number theory to do more.