@Jonathan Lee Thanks for posting in our Q&A.
For this issue, I have done the test in my lab. It shows as same as yours. The configuration profile shows "succeeded" in intune portal. And the key is successfully added in registry editor. However, this "configure favorites" isn't listed under Microsoft Edge Policies.
Given this situation, it is needed to do log analysis to find whether this root cause is on intune or on Edge. With Q&A limitation, it is suggested to create an online support ticket to solve this issue. It is free. Here is the support link:
https://learn.microsoft.com/en-us/mem/get-support
Thanks for understanding and hope everything goes well with you.
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