Right now, the images contain the Ubuntu 24.04LTS version of barman - 3.10.
Ubuntu 24.04 also comes with python 3.12. As far as I understand, barman 3.10 comes with a bug when run under python 3.12 where it won't delete the local files until after the backup EnterpriseDB/barman#1076 - that seems to make it essentially unusable with the 10GB root volume fly provides, as soon as the database is larger than 10 or so GB?
Barman's official distribution method is in the postgres repository - moving apt install barman to after adding the postgres repository gives barman 3.16 instead.
Therefore, the easiest fix seems to be to just add the postgres repository before installing barman. Would a patch to do that be accepted? I recognise that would essentially unpin the barman version.