Is it normal for the Julia language server to take ~20 s to start up?

Yes, please try upgrading. Either do this

Or upgrade in place (no change needed in you configuration in this case):

shell$ cd /home/tokujin/.emacs.d/elpa/eglot-jl-20230601.1335/
shell$ julia --project=. -e 'import Pkg; Pkg.update()'

(I’ve copied the correct path from your eglot output above)

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