I have 400 gigabytes available for storage on the server, why am I not able to save a new project?

If you have 400 GB free on the server, then there is plenty of space for new projects on the server itself. I think the limit must be set somewhere else. Most likely the limitations are set on the file size of the database files. These can be changed in SQL Management studio, see pictures below. Remember that the MassTrack project databases comes in pairs, and so you should also check the _Log database which may be larger than the original one, and that deleting a project actually does not delete it from the log database (this can be done manually if needed).

Finally, note that even if you delete out rows in a database, the size of the database file may not always shrink accordingly. You may have to manually run shrink commands in SQL Management Studio (see last picture). It may be that if you run shrink command, that is all you have to do to make room for more projects.