I'm putting this here for my own reference because I was up way too late figuring this out.
After installing the network card, I could see I already had the right driver for it. sudo lshw -c network
showed that the card was disabled though. What ended up getting the card working was the following which I recorded here:
sudo ip l s dev enp6s0 up
Then I modified /etc/netplan/01-network-manager-all.yaml
to look like this:
network:
version: 2
renderer: NetworkManager
ethernets:
enp6s0:
match:
macaddress: "12:34:56:78:90:12"
set-name: enp6s0
dhcp4: true
dhcp-identifier: mac
critical: true
nameservers:
addresses: ["<LAN IP address of router>"]
Then
sudo netplan --debug generate
sudo netplan apply
sudo reboot
That got the card working correctly. Then the instructions on Ubuntu's WakeOnLan page worked seamlessly for me to get Wake-on-LAN.