There isn’t currently a way via Web or Insight. The CLI’s omero fs usage reports a total for the given container and, for instance, something like,
omero hql --style plain "SELECT id FROM Dataset" | cut -f 2 -d ,
should yield a list of IDs to loop over.
This CLI disk usage command simply uses Blitz’s DiskUsage2 and one could upload a script that uses that and reads and writes map annotations to annotate each container with its current space usage. It would require a bit of script-writing but this would be a great introductory project that shows one of the many ways in which one can enhance one’s OMERO installation.
Note that the ability to link the same image into multiple datasets, or the same dataset into multiple projects, could cause some “double counting”, where deleting only the last reclaims the space. Further, data imported in-place is counted as if they were simply uploaded in full.