I think I got it working! I couldn't access the Proxmox web interface anymore either no matter what I tried so I reinstalled Promox entirely. After reinstalling it still didn't work, so I tried again using another subnet in the network configuration during setup, and manually connecting my laptop to that subnet. After that I was able to access the Proxmox web interface again, so I continued following the steps like I did before. I was now able to connect to the pfSense interface too. I think the issue was with DHCP not working yet because the setup of pfSense in the web interface wasn't completed yet; the new subnet I used is the same subnet I used for pfSense (192.168.1.x), so that's probably why I was able to connect now.
For now I can't test any further until tomorrow because our switch is in my parents bedroom, and they're asleep now. I did test another laptop and that did immediately get an IP within the subnet, it also was able to connect to the internet.