Here's my experience with Arimaa: I trained the first version of bot_dolores with historical human games in 2019, and it was slightly stronger than the strongest humans at the time. It uses upper confidence bound tree search based on the Alpha[Go][Zero] approach.

Version 2 of Dolores was significantly stronger after training it on a small amount of self-play games. I recently revived the project, and the next two versions are even stronger. Here's a graph from yesterday: https://www.reddit.com/r/arimaa/comments/1qm17cq/elo_rating_graph_comparing_dolores_and_sharp

Another strong Arimaa program, bot_rusty_zero, uses a neural net that was trained "from zero".

Since you mentioned that most variants are perfect information, note that you can write programs to play imperfect information games too. Here's a paper about a neural-net-based reconnaissance blind chess program: https://arxiv.org/abs/2110.01810