Is it possible to run the notebook using a Julia Project.toml
Yes, make this your first cell:
import Pkg
Pkg.activate("/path/to//Project.toml")
You’ll need to add a MUMPS_seq_jll = "5" line to the [compat] section of your Project.toml.
Your other option is to use a local copy of SigmoidalProgramming.jl with some edits.
import Pkg
Pkg.dev("SigmoidalProgramming")
Then look in ~/.julia/dev/SigmoidalProgramming and edit the Project.toml to update the bounds to:
[compat]
julia = "1.6"
Clp = "1"
DataStructures = "0.18"
GLPK = "1"
JuMP = "1"
MathOptInterface = "1"
It looks like a simple package, so that might be enough.