The transaction log for database 'database' is full due to 'LOG_BACKUP'. Nothing works
Performing full database backups does not truncate the transaction log.  In order to truncate the transaction log you have to perform a transaction log backup.  If you changed the recovery model to simple and still received the error, then this means you had active transactions that could not be cleared by checkpoint.

Relying on autogrow for capacity planning is not a good idea.  A better idea is to set your transaction log large enough so that auto grow does not occur.  I don't see where you tried to manually increase your transaction log size in your troubleshooting steps, nor do I see where you tried to perform a transaction log backup.

Another thing you could have tried is to add another transaction log file, just to see if that would resolve the error and allow processing to continue.  I would remove that additional file after completing my troubleshooting.

There are a lot of possibilities here, so I would recommend setting the log size larger than it was before, change the autogrow settings larger than 1mb and set up frequent, regular transaction log backups to keep the tranlog size on the smaller side.

If you don't want to mess with tranlog backups, then keep the recovery model on simple, but realize this means you will only be able to restore back to your last full backup, and it is still possible for a tranlog to fill up when in simple recovery mode.