I have no idea why your project stopped working. The dependencies do not change unless you explicitly ask for it (or change Project.toml manually).
Uh, I am out of my depth here. Let’s try to collect more information about the packages and their extensions:
julia> using Pkg
julia> Pkg.status(extensions=true, mode=PKGMODE_MANIFEST)
This lists all the dependencies of your package together with their extensions and the dependencies of the extensions.
Edit: FWIW, I can add ControlSystems to a fresh environment without any issues in julia 1.10. Since you see the error in a fresh environment with a clean ~/.julia, then I can only imagine something’s wrong with the Julia installation on your cluster. Perhaps something has changed over the weekend? Maybe you could install juliaup (GitHub - JuliaLang/juliaup: Julia installer and version multiplexer) and install julia to your home directory?