Your C code and Makefile are fine. This is what I get with those files:
$ make
gcc -c -Wall -fPIC calc_mean.c -o calc_mean.o
gcc -shared -fPIC -o libmean.so calc_mean.o
$ julia
_
_ _ _(_)_ | Documentation: https://docs.julialang.org
(_) | (_) (_) |
_ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help.
| | | | | | |/ _` | |
| | |_| | | | (_| | | Version 1.8.0 (2022-08-17)
_/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release
|__/ |
julia> ccall((:mean, "./libmean.so"), Cdouble, (Cdouble, Cdouble), 1.0, 2.0)
1.5
I agree that something seems to be strange with your Julia installation and/or runtime environment.