Simple solution using modulo arithmetic and arrays. Relies on python shorthands that hides implicit branches for the number case though.

    def main():
      fizz_array = ["Fizz", "", ""]
      buzz_array = ["Buzz", "", "", "", ""]

      for n in range(1, 101):
        # Use modulo to index into arrays
        f = fizz_array[n % 3]
        b = buzz_array[n % 5]

        # Combine fizz and buzz
        result = f + b
    
        output = result + str(n)[len(result):]
    
        print(output)
    
    main()

I couldn't figure out this line and had to rely on AI for it.

    output = result + str(n)[len(result):]