@Sterling, G Thanks for posting in our Q&A.
Intune can configure kiosk mode in iOS devices. However, the iOS device should be ADE enrollment and put into supervised mode.
https://video2.skills-academy.com/en-us/mem/intune/configuration/device-restrictions-ios#kiosk
For this feature that the browser resets back to the main page when there is no activity, it seems that there is no such setting in intune. If you are interested in this feature, it is suggested to post in intune feedback portal. It is a place to collect customers' requirements and problems. Here is the link:
https://feedbackportal.microsoft.com/feedback/forum/ef1d6d38-fd1b-ec11-b6e7-0022481f8472
Thanks for your understanding.
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