To enable Steam Local Network transfer, first ensure to allow it in your settings

Steam --> Downloads --> Game File Transfer over Local Network

Next, you need to enable the appropriate ports on BOTH computers

Run:
sudo ufw enable
sudo ufw allow 27040/tcp
sudo ufw allow 27031:27036/udp

Then start the transfer by downloading the files on the target machine. For more info, see https://psteamhelp.yuanyoumao.com/en/faqs/view/46BD-6BA8-B012-CE43