> find /usr/bin -atime +360 | xargs -l1 apt-file find | sort

I would suggest dpkg -S instead of apt-file find, which matches prefix,
not exact file. I would also filter on the package name and ensure
unicity. Also, never log in as root.

Here would me my quick & dirty take at your command chain:
find /usr/bin -atime +360 | xargs -l1 sudo dpkg -S | awk -F ':' '{print
$1}' | sort | uniq

Bernard (Beer) Rosset
https://rosset.net/