From Server < Backups, you can specify to clean backup files older than certain days while creating/updating a backup (Available for local backups). Setting this up will run the cleaning job every mid-night and clean the backup files older than certain days.
I think you’ve already tried it out, if not do give it a try so that you’ll not have to face storage issue because of old back up files again.
To solve it right now, you’ll have to SSH into the server and get rid of some of the old backup files.