非常に有益な情報ありがとうございます。
cleanup を実行する前に、Discourse はリストアを行わずにバックアップの整合性を検証する方法を提供していますか？
du -hx / | sort -h | tail -49 の出力結果です（-h を使うと結果を解析しやすかったので使いました）:
833M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/42/fs/var/www/discourse/vendor/bundle/ruby
833M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/42/fs/var/www/discourse/vendor/bundle/ruby/3.4.0
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www/discourse
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www/discourse/vendor
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www/discourse/vendor/bundle
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www/discourse/vendor/bundle/ruby
837M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs/var/www/discourse/vendor/bundle/ruby/3.4.0
839M /var/discourse/shared
839M /var/discourse/shared/standalone
840M /var/discourse
863M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/42
863M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/42/fs
868M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283
868M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/283/fs
874M /var/lib/containerd.io.containerd.snapshotter.v1.overlayfs/snapshots/284
874M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/284/fs
874M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/43
874M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/43/fs
908M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/263/fs/usr
925M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/22/fs/usr
944M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/263
944M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/263/fs
961M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/22
961M /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/22/fs
1.3G /usr
1.4G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/251
1.4G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/251/fs
1.4G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/251/fs/var
1.4G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/251/fs/var/www
1.4G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/251/fs/var/www/discourse
1.5G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/227/fs/var
1.5G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/227/fs/var/www
1.5G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/227/fs/var/www/discourse
1.6G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/227
1.6G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots/227/fs
2.5G /var/log
2.5G /var/log/journal
2.5G /var/log/journal/1d9299c9656046d6bd0e18d4a09c183c
2.7G /var/lib/containerd/io.containerd.content.v1.content
2.7G /var/lib/containerd/io.containerd.content.v1.content/blobs
2.7G /var/lib/containerd/io.containerd.content.v1.content/blobs/sha256
9.8G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs
9.8G /var/lib/containerd/io.containerd.snapshotter.v1.overlayfs/snapshots
13G /var/lib
13G /var/lib/containerd
17G /var
20G /
docker volume ls -qf dangling=true の出力は空でした。実際、docker volume ls も空です。
docker images -a の結果:
IMAGE ID DISK USAGE CONTENT SIZE EXTRA
discourse/base:2.0.20260209-1300 50d2dae489a9 4.77GB 1.12GB
discourse/base:2.0.20260521-0047 27373b823bbe 4.89GB 1.17GB
local_discourse/app:latest 01527763be8d 6.9GB 1.63GB U
Docker について知識が不足しており、この出力を診断できませんが、単なるログであれば /var/log/ が少し大きすぎるように思えます。また、現在稼働しているフォーラムは 1 つだけなのにイメージが 3 つあるのは興味深いです（もちろんこれは想定内のことかもしれません）。
ストレージ容量を増やすという点については理解しました。おそらく容量を増設すると思いますが、その前に良い学習機会となりました。