@HenryZhang-6712,
I'm glad that you were able to resolve your issue 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.
Issue:
Customer was able to setup the "Diagnostic Settings" under the API Management Service. However, they could not enable "Azure Monitor" for their API, it keeps
asking them to enable diagnostic settings despite already having done so.
Solution:
Customer was able to resolve the issue by renaming the "Diagnostic Setting" and successfully enabled Azure Monitor Diagnostic logs.
Thank you again for your time and patience throughout this issue.
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Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.
Thanks,
Carlos V.