Run the old system but namespace the new glibc:
Run this to see what depends on your current libc6: upgrade libc6 to 2.34
If you try to force an install of libc6 2.34 on a system built for 2.31 (like Ubuntu 20.04), the package manager will scream. It will warn you that essential tools will break, and if you proceed blindly, you might find yourself with a system that cannot boot or accept input. Run the old system but namespace the new
wget http://archive.ubuntu.com/ubuntu/pool/main/g/glibc/libc6_2.34-0ubuntu3_amd64.deb sudo dpkg -i --force-depends libc6_2.34-0ubuntu3_amd64.deb and if you proceed blindly
find /usr/bin /usr/sbin -type f -executable -exec ldd {} \; 2>&1 | grep "not found"
ldd --version # Should output: ldd (GNU libc) 2.34