For me a 128gb SD card was filling up, but there were no big files in the container.
I had to use the community web ssh terminal by Frenck in HACS.
With it, you can login using SSH and then connect to the supervisor docker container. Disable protection mode in the addon settings.
Docker ps (to find the containers)
Look for the container ID of the supervisor container.
docker exec -it CONTAINERID /bin/bash (login to container)
du -a / | sort -n -r | head -n 20 (find big files)
In my case there were redundant backup files in /mount/data