This was happening to me. In my case, it was the DDNS container. Stopping it solved my issue. Now I just need to figure out why it is filling the folder.
The process I used to determine which container was using all the space,
Log into the terminal
Determine if /run is full by running df
Figure out which directory is using the space by running du /run
In my case it was /run/docker/containerd/daemon/io.containerd.runtime.v2.task/moby/d0d2f1fc260167b0504709e92ee78b602a3acc9837735feff0d751c5cf55283d
Take a look in the directory to see what is taking up the space so you can fix it later. In my case it was thousands of .pid files
Note the hash, that is the container id
Run docker container ls
The first 12 characters from the hash should line up with one of the running containers listed
Kill the offending container
Fixed, buy yourself a beer