Stefan Rehnberg I'm glad that your issue is resolved and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that the question author cannot accept their own answer, they can only accept answers by others, I'll repost your solution in case you'd like to Accept the answer.
Error Message:
Azure AI Custom Translator
Uploading training files that uploaded fine a week ago, now fails with error: "Uploading 'TMXFile' failed
Double check that your documents meets all requirements. If the issue persists, contact us at aka.ms/translatorsupport."
Solution:
I further verified internally and not found any issue.
As you confirmed that the issue is resolved, This seems to be a transient failure.
If you have any other questions, please let me know. Thank you again for your time and patience throughout this issue.