We typically run, test, and recommend Ubuntu LTS versions (currently 24.04) so it could be something with Ubuntu 25.04 or your specific system/setup. Unfortunately we had issues installing Ubuntu 25.04 in our VMs so can't test it at the moment.
Assuming it has installed it should by default have created a "~/local" folder with the subfolders "MATLAB" and "Precise_Simulation", so you can start the toolbox with the command:
~/local/Precise_Simulation/FEATool_Multiphysics/application/run_FEATool_Multiphysics.sh local/MATLAB/MATLAB_Runtime/v97/