What must a person do who has repented to Allah but is unable to delete songs they previously uploaded to YouTube, having forgotten their login information, and all their attempts to delete them have failed?

As long as you have repented to Allah with sincere repentance and have exerted your utmost effort in trying to remove the traces of the sin, then you have done what you are capable of. Allah does not burden a soul beyond its capacity. Therefore, there is nothing upon you, and you will not incur sin for listening to these songs.