First, make sure the chat status is actually Complete. If another status is in place (due to a bug, for example), the transcript won't be correctly filled. Transcripts may take some minutes to update to Completed.
If this is not the case, the information load might have failed. You may want to try and refresh the Unbabel fields. Click Edit on the Unbabel Translated Body and then Save the Chat Transcript. The Unbabel Translated Body should auto-populate.
Note that for the Chat transcript to update successfully, the user who is considered to make the last update on the chat - be it the agent handling it or an automated user you have in place must have the correct permissions for the Chat Transcript object.
If this is not the case, it is time to reach out to us at firstname.lastname@example.org. Please make sure to send us a report on the translation requests contained in the chat conversation so we are able to investigate.