/usr/lib/x86_64-linux-gnu/libgnutls.so is in libgnutls-dev 3.4.10-4ubuntu1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libgnutls.so.30.6.2
/usr/lib/x86_64-linux-gnu/libgnutls.so.30.6.2