Disclaimer - I’m no DBA, so take this with a grain of salt…
That’s a slightly different error, still related to the transaction log… I did find at least one related SQL bug, you might have your DBA check whether you are impacted by https://support.microsoft.com/en-us/help/4132896/kb4132896-transaction-log-full-when-space-available-autogrowth-enabled
If you aren’t affected by this issue, the general resolution steps are at https://docs.microsoft.com/en-us/sql/relational-databases/logs/troubleshoot-a-full-transaction-log-sql-server-error-9002 but your DBA probably has these already.
If the database recovery model is set to “full” rather than “simple”, then space in the transaction log cannot be reused until a database log backup runs. In “full” recovery mode, after restoring a full or differential database backup, you could replay the transaction logs to recover the database all the way up to the point-in-time of a failure; where I’ve used Full Recovery mode, we would take Transaction Log backups frequently (like every 15-30 minutes).
Usually, Full Recovery mode is overkill for BFI. We aren’t running credit card/banking transactions, if the server fails we’d just restore the previous day’s backup and run a new Import. If you have the DBA change the database’s recovery model to Simple, the Transaction Log space can overwrite itself as needed for any new transaction, it doesn’t require log backups before reclaiming the space.
I don’t know your specific needs, but I’d usually just set the BFI database for Simple Recovery and let it overwrite the transaction log as needed, take daily full backups, and not have to deal with transaction log backups.