Thanks, I managed to compile a system image. Now the REPL starts almost instantly. There is a small error in the very helpful instructions by the github user nlw0: the command
julia preco.jl --startup-file=no --trace-compile=myprecostatements.jl
does not produce any precompile output, at least for Julia 1.7.3, because the command-line switches must appear before the script name, otherwise they get interpreted as command-line arguments for the script instead of Julia itself. So you need instead
julia --startup-file=no --trace-compile=myprecostatements.jl preco.jl
After going through the steps, I also have to modify julia-snail.el to start Julia using the newly compiled system image.
It would be nice if JuliaSnail.jl is distributed as a standalone Julia package, which would make it easier for users to generate system images.