Hi @Wolfgang Knupp,
I'm glad to hear that your issue has been resolved. And thanks for sharing the information, which might be beneficial to other community members reading this thread as solution. 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 ", so I'll reiterate your response to an answer in case you'd like to accept the answer. This will help other users who may have a similar query find the solution more easily.
Query: Azure AI Studio: How to delete a failed vector index?
Solution: In the indexes list, click on the link of the failed index that you want to remove, this takes you to the ML job that failed. Delete the failed ML job. (confirm deletion with yes) - once this is gone, the failed index in Azure ai studio will also disappear.
If you have any further questions or concerns, please don't hesitate to ask. We're always here to help.
Do click Accept Answer and Yes for was this answer helpful.