There's a lot of ways you can do it. I think it's fun to see how people solve it when they're not allowed to use the obvious answers (note: I don't interview people and probably would not choose no-modulo-fizzbuzz as an interview question).

Similar to your solution, instead of two counters, you can have two iterators that cycle every 3 / 5 elements, and add them. Then fill in any blank elements with their index+1.

    from itertools import cycle, zip_longest, islice
    
    fizz_list = ['', '', 'fizz']
    buzz_list = ['', '', '', '', 'buzz']
    output = [
        fizz + buzz for fizz, buzz
        in islice(zip_longest(cycle(fizz_list), cycle(buzz_list)), 0, 100)
    ]
    for i in range(len(output)):
        print(output[i] or i+1)