@Anton A. Tatarkin Thanks for posting in our Q&A. From your description, did you mean that you only want to use Microsoft Edge Browser in your Android device? If there is anything misunderstanding, please correct me.
For this issue, there is no method to set "Stay in Microsoft Edge" via intune. However, we can use the app protection policy to make some content opened by Edge. We can select "Microsoft Edge" in Restrict web content transfer with other apps in the app protection policy and add Edge and any other apps as protected apps, when we open some web links in these protected apps, it will be opened by Edge.
https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-android
However, if the apps are not added in the app protection policy, it will not be opened by Edge.
Thanks for your understanding.
If the answer is the right solution, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.