Project administrators can enable per-project storage from the manage project link on the sidebar.

You can put stuff in /data/project (ideally in subfolder, since it's shared)

No, I can't:

magnus@wikidata-wdq-mm:~$ touch /data/project/testing
touch: cannot touch `/data/project/testing': Permission denied

magnus@wikidata-wdq-mm:~$ groups
wikidev project-bastion project-wikidata-dev project-analytics project-tools

So, could anyone give me permissions to write to /data/project? Please?

/data/project is mounted storage and appears to be owned by root. This is apparently how it is supposed to work, per chat on Cloud-Services

People in the project can sudo and then create a directory. Then you can change the permissions for it.

Thanks, that worked!