> It seems that the strategy is to use the neural network to score various moves and then a search strategy to try to find moves that result in a favourable score
There is a LOT of cleverness built into the stockfish search as well.
In fact, while neural networks have now won the position evolution game, it is still an open discussion in the chess programming community if the Alpha Zero / Leela search (NN + Monte Carlo) is as good as Stockfish's PVS.
The neural net is only for scoring positions, not moves. Check the article on Stockfish NNUE at the chess programming wiki: https://www.chessprogramming.org/Stockfish_NNUE
There is a LOT of cleverness built into the stockfish search as well.
In fact, while neural networks have now won the position evolution game, it is still an open discussion in the chess programming community if the Alpha Zero / Leela search (NN + Monte Carlo) is as good as Stockfish's PVS.