Interesting, the stand-alone installer is supposed to automatically download and install the Matlab Compiler Runtime (MCR) directly from the Mathworks (rather than bundling 8-9GB). So I'm guessing the issue is on their end, or some gateway between you and them, not quite sure.
The workaround would be to first download and install it manually from (the toolboxes are currently compiled against the 2019b (9.7) version, others will most likely be incompatible with FEATool/CFDTool):
Once the MCR is installed and detected, hopefully the runtime will skip the download dependencies step, and just install the toolbox. However, if it does not the workaround here would be to simply extract the actual toolbox binary and run it manually (the installer is a zip archive).
# Run the executable with
run_FEATool_Multiphysics.sh "path_to_matlab_mcr_runtime" # for example /home/user/MATLAB/MATLAB_Runtime/v97