What makes you think the saves are still 0.13.9?
Yes, the savefiles record which version they were made on, but if you can load them then they're working fine.
Otherwise it would throw a very obvious error message.
Is it because of the "no more content in this version" messages?
Well, if you read the changelogs you would find out that the message may still be true in the latest version.
That's just how it is, nothing wrong with your save, thing just doesn't have more content.