UnraidC

I don't know why exactly, but this (or one of the things below) is what solved it in the end:
I noticed that docker.img had grown >50gb (which is not normal from what I found on reddit somewhere as I only run a few dockers). I removed all dockers via the "Docker" tab in Unraid. I stopped the docker service (under "settings -> docker"). I tried to delete the docker.img via the option in the same menu after turning docker off, but nothing happened (was following these instructions: https://docs.unraid.net/unraid-os/manual/docker-management/#re-create-the-docker-image-file), i.e. the file remained in place, even after several tries. I then tried to delete the file directly via system/docker/docker.img (going via the "Share" tab in Unraid) but whenever I hit delete nothing happened either (i.e. the file just remained in place). I rebooted the server, leaving the docker service off. I then tried again to delete the file (same as in step 5). This time it did delete and the system/docker/ folder ended up empty. I then used the "Cleanup Appdata" plugin to remove all of the appdata paths shown there (except for 3 which I was quasi sure were not the ones causing issues as they never did before) I reinstalled most dockers, except nginx and traefik. Remote access to server was working again - problem solved.  
So in the end it seems one of the dockers or some combination was causing issues (I still assume it was something related to Nginx or maybe Traefik even though I did almost nothing with the latter). Before doing the above I had already just tried deleting different dockers etc. but that did not resolve it.
 
Cannot say why it worked but it did, so maybe it can help somebody else as well at some point without wasting hours of your life on it.
 
In closing, thank you @JorgeB for taking the time and effort to think along with me, I appreciate it!