>But you can perform minimax (which is how AlphaZero works)
AlphaZero uses Neural Networks, old engines used to use Alpha-Beta pruning if I am not mistaken but after 2017 (the year AlphaZero papers were released) they started using a combination of the two or just NN.
Chess Programming Wiki [1] is an awesome website if you want to learn how Chess engines work in detail (or write one).