SQL Server 2016: Table can't grow while 313 MB is still available in the database
You mentioned you don't expect the delete operation to have released space but that is not the case. Pages that are emptied as a result of the delete become unused space (which may be reused for the same object) and emptied extents become unallocated space (which may be used for any object).
Consequently, the DELETE looks to have freed enough space within the data file to avoid the space problem. Consider reorganizing the indexes to further reclaim space from partially filled pages since your database is still over 95% full.