Oh, sorry, maybe instead, can you try setting JULIA_PKG_SERVER explicitly? I guess it needs it even to check the dependencies.
Maybe try the Nanjing University one from the PkgServerClient.jl list, which looks to be live: NJU Mirror
julia> ENV["JULIA_PKG_SERVER"] = "https://mirrors.nju.edu.cn/julia";
julia> using Pkg
julia> Pkg.Registry.update()
If that works, you can set it globally in your environment variables. Maybe the PySR installation will “just work” then.