This is because you have some old versions not cleaned up while upgrading gcc.

First of all, make sure that you have the latest lib with conda install -c conda-forge libstdcxx-ng

1. Find all your lib versions with find / -name "libstdc++.so*". My latest version is 6.0.30.

/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.29
/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0
/usr/lib/gcc/x86_64-linux-gnu/9/libstdc++.so
/usr/lib/gcc/x86_64-linux-gnu/9/libstdc++.so.6.0.29
/usr/lib/gcc/x86_64-linux-gnu/9/libstdc++.so.6.0
/opt/conda/lib/libstdc++.so.6.0.29
/opt/conda/lib/libstdc++.so.6
/opt/conda/envs/xxx/lib/libstdc++.so.6.0.30
/opt/conda/envs/xxx/lib/libstdc++.so.6
/opt/conda/pkgs/libgcc-7.2.0-h69d50b8_2/lib/libstdc++.so.6.0.21
/opt/conda/pkgs/libstdcxx-ng-12.1.0-ha89aaad_16/lib/libstdc++.so.6.0.30
/opt/conda/pkgs/libstdcxx-ng-12.1.0-ha89aaad_16/lib/libstdc++.so.6
/opt/conda/pkgs/libstdcxx-ng-12.1.0-ha89aaad_16/lib/libstdc++.so

2. Copy the file to the folder where you are working at and only have the old versions. /opt/conda/lib/ or /opt/conda/envs/xxx/lib/

For example, I'm working on /opt/conda/lib/

cp /opt/conda/pkgs/libstdcxx-ng-12.1.0-ha89aaad_16/lib/libstdc++.so.6.0.30 /opt/conda/lib/

3. Remove the old files and link the latest lib. Please repeat these steps for other folders.

cd /opt/conda/lib/
rm libstdc++.so.6.0.29
rm libstdc++.so.6.0
ln -s libstdc++.so.6.0.30 libstdc++.so.6

Just to share, not sure it will help you. However it shows that in standard conditions it is possible to use the conda gcc as described in the documentation instead of the system gcc.

# system gcc
which gcc && gcc --version
# /usr/bin/gcc
# gcc (Ubuntu 9.3.0-17ubuntu1~20.04) 9.3.0

# creating a conda env with gcc
conda create -n gcc gcc
# activate the environment
conda activating gcc
which gcc && gcc --version
# /opt/conda/envs/gcc/bin/gcc
# gcc (GCC) 11.2.0

Here is the list of packages installed on a fresh environment created with only gcc.

# packages in environment at /opt/conda/envs/gcc:
#
# Name                    Version                   Build  Channel
_libgcc_mutex             0.1                 conda_forge    conda-forge
_openmp_mutex             4.5                       1_gnu    conda-forge
binutils_impl_linux-64    2.36.1               h193b22a_2    conda-forge
gcc                       11.2.0               h702ea55_2    conda-forge
gcc_impl_linux-64         11.2.0              h82a94d6_11    conda-forge
kernel-headers_linux-64   2.6.32              he073ed8_15    conda-forge
ld_impl_linux-64          2.36.1               hea4e1c9_2    conda-forge
libgcc-devel_linux-64     11.2.0              h0952999_11    conda-forge
libgcc-ng                 11.2.0              h1d223b6_11    conda-forge
libgomp                   11.2.0              h1d223b6_11    conda-forge
libsanitizer              11.2.0              he4da1e4_11    conda-forge
libstdcxx-ng              11.2.0              he4da1e4_11    conda-forge
sysroot_linux-64          2.12                he073ed8_15    conda-forge