The solution turned out to be run manually
InstallMathWorksServiceHost
as the local which lives in ~/.MathWorks/ServiceHost/-mw_shared_installs/v2025.5.1.1/mci/bin/glnxa64 (obviously, the version might be different).
This discussion got me on the right way https://uk.mathworks.com/matlabcentral/answers/2176458-failed-to-run-matlab-gui-in-fedora-42 although the location of the installer has changed in 2025a.