I wrote several polyomino solvers for this project:

https://www.oranlooney.com/demos/soma-forest/

One of them used constraint solving with Z3, which was indeed reasonably fast. However, by far the fastest was a simple backtracking solver written in Rust which used bit twiddling to quickly test for intersections. For polyomino's in particular, this represents between 10x and 100x constant speed boost, depending on the size of board. There's no way to get that back with a smarter solver.