I was able to solve it with the help of a user on Reddit. Even though the configuration looked correct, the Unifi controller container was running a bad create command and using my proxynet instead of Bridge mode. So, I migrated my Unifi controller to another instance of it on Br0 with a different static IP address, and that worked like a charm.
I have a Nextcloud docker setup on my Unraid server (ver. 6.9.0) & a recent Unifi controller as well. I have set up the Nextcloud server as per Spaceinvaderone's video instructions.
All was fine until I moved to a new house and set up the Unifi controller, and now when I access my URL (Or even use "WebUI" from the Docker menu) it directs to my Unifi landing page instead of the Nextcloud UI. I believe this is probably an issue with port mapping, but I made sure that no ports overlap. No changes were made to my config files for SWAG either. As a side note, this happens even when the Unifi docker container is stopped.
Relevant Port allocations:
mariadb: 172.17.0.4:3306/TCP <-> 192.168.1.3:3306
nextcloud docker: 0.0.0.0:443/TCP <-> 0.0.0.0:444
swag: 0.0.0.0:443/TCP <-> 0.0.0.0:1443
0.0.0.0:80/TCP <-> 0.0.0.0:180
unifi controller: 172.17.0.6:10001/UDP <-> 192.168.1.3:10001
172.17.0.6:3478/UDP <-> 192.168.1.3:3478
172.17.0.6:8080/TCP <-> 192.168.1.3:8080
172.17.0.6:8443/TCP <-> 192.168.1.3:8443
172.17.0.6:8843/TCP <-> 192.168.1.3:8843
172.17.0.6:8880/TCP <-> 192.168.1.3:8880