Hide symbol and source file name in C static library using cmake

I found a lot of questions on the hidden symbol topic in C static library. I tried a lot of things:
-> Add strip and optimisation -O3 -s CFLAGS
-> Add -Wl,--exclude-libs,ALL" "-Wl,-Bsymbolic LDFLAGS
-> Add -fvisibility=hidden and __attribute__ ((visibility ("hidden")))

I cannot make it work properly. Instead of a long explanation, nothing is better than a project example using a very simple source tree to demonstrate my issue: https://github.com/Evanok/static_library_hidden_test

In this repository, I am using CMake to generate a static library. The only public API is in tutu1.h. I also add a test directory to validate the linking and execution of the library with a main.

I was able to hide the source file name using a post bash-script, but I cannot hide symbols in the final static library file.

This is the current result:

rm -rf build/ && cmake -DDEBUG=OFF -B build -S . && cmake --build build && nm build/libtutu.a
(...)
[100%] Built target static_tutu_library

private_sklock0.o:
0000000000000000 r .LC0
                 U normal_tutu3_function
                 U __printf_chk
0000000000000000 T this_is_the_only_public_function_tutu1

private_sklock1.o:
0000000000000000 r .LC0
0000000000000000 r .LC1
                 U __printf_chk
0000000000000000 T unused_tutu2_function

private_sklock2.o:
0000000000000000 T normal_tutu3_function

I expect only the function this_is_the_only_public_function_tutu1 to be visible in my symbol/library definition list.

EDIT1:

Answer from the comment section -> This is not possible. Indeed after checking documentation from https://gcc.gnu.org/wiki/Visibility about hidden feature. This feature is only valid for shared library. Not static library.

EDIT2:

I run the test on a shared library. I was able to hide everything by using the CFLAGS -fvisibility=hidden + the attribute ((visibility ("default"))) on my public API.

If you want to test the result with shared library, I created a branch here that is using cmake shared library example instead of static one: https://github.com/Evanok/static_library_hidden_test/tree/shared_library

EDIT3:

This is also a script I am using to hide all the object filename, $1 is the argument of the script. It should be the original static library file:

[arthur] cat hide_object_name.sh
#!/bin/sh

i=0
echo "lets hide symbol from $1"
rm -f *.o *.obj *.c.obj
ar xv "$1"

for f in $(ls *.obj); do
  if [ -f "$f" ]; then
    echo "process $f.."

    extension="${f##*.}"
    new_name="private_$i.$extension"
    echo "rename $f as $new_name"
    mv "$f" "$new_name"
    i=$((i + 1))
  else
    echo "File $f not found."
  fi
done

rm -f "$1"
echo "generating new library $1..."
ar crs "$1" private_*.*
rm -f *.o *.obj *.c.obj
sync