Having installed a LEMP stack (nginx) on Ubuntu 20.04 I can run a fresh Wordpress site in Firefox using the IP address 127.0.0.1 with no problems. Using 'localhost' doesn't work.

From another Ubuntu 20.04 in my home network I use the IP address 192.168.0.213 and get just a bare-bones view of the Wordpress site. The HTML shows me that all the links in this case contain the hostname 127.0.0.1 like in my first case.

Do I need to have a DNS Server in my simple home network - which I think would be an overkill - or what else can I do ?