@Patrick Pedersen Thanks for posting in our Q&A.
Based on my research about intune's app feature, currently, there is no such feature to make safari or Chrome default browser in intune managed iOS or Android devices via intune.
From your description, I know that Edge opens Links that from Teams or Outlook. Please check if we add Teams and Outlook in the app configuration policy and set "com.microsoft.intune.useEdge true" in the same app configuration policy.
If there is anything update, feel free to let us know.
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