TODO didn't manage to get it working with TP Link ARCHER VR2800 even though it shows DHCP as enabled and it also shows MAC addresses and corresponding hostnames in the router management interface.
For IP-level communication, askubuntu.com/questions/22835/how-to-network-two-ubuntu-computers-using-ethernet-without-a-router/116680#116680 just worked between P51 and P14s both on Ubuntu 23.10 connected with a regular Cat 5e cable.
On both machines, first we found the Ethernet cable interface name with the ip CLI tool:
ip a
which outputs on the P41s:
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
    inet 127.0.0.1/8 scope host lo
       valid_lft forever preferred_lft forever
    inet6 ::1/128 scope host 
       valid_lft forever preferred_lft forever
2: enp1s0f0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP group default qlen 1000
    link/ether fc:5c:ee:24:fb:b4 brd ff:ff:ff:ff:ff:ff
3: wlp2s0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc noqueue state UP group default qlen 1000
    link/ether 04:7b:cb:cc:1b:10 brd ff:ff:ff:ff:ff:ff
    inet 192.168.1.123/24 brd 192.168.1.255 scope global dynamic noprefixroute wlp2s0
       valid_lft 61284sec preferred_lft 61284sec
    inet6 fe80::3597:15d8:74ff:e112/64 scope link noprefixroute 
       valid_lft forever preferred_lft forever
so the interface was enp1s0f0, because wlp is wireless and lo is localhost.
So on the P14s we assign an IP of 10.0.0.10 to the P51:
sudo ip address add 10.0.0.10/24 dev enp1s0f0
Then on the P51 analogously, giving IP of 10.0.0.20 to the P14s:
sudo ip address add 10.0.0.20/24 dev enp0s31f6
And after that, P14s can:
ping 10.0.0.10
and P51 can:
ping 10.0.0.20
TODO after a few seconds, the settings appear to be forgotten, and ping stops working unless you do sudo ip address add on the local machine again. This seems to happen after a popup appears saying "Activation of network connection failed" as it fails to obtain Internet from the cable.
TODO list and delete such manual assignments we've made.
E.g. to give Compueter 2 Internet in a setup like:
Internet --- Wi-Fi --- Computer 1 --- Ethernet --- Computer 2
Can be tested e.g. by turning off Wi-Fi from Computer 2 if it has one.