If I have a subscription based app that's available on iOS, Android, and the web.I use the appropriate billing systems for each platform (Apple IAP for iOS, Google Play Billing for Android, and my own system for web) What happens when a user subscribes on Android or the web, then logs into the same account on the iOS app? Am I allowed to honor that existing subscription on iOS, or am I required to have them purchase a separate subscription through Apple’s in app purchase system in order to access premium features on the iOS app?
Absolutely, many small and larger apps offer their services across multiple platforms. Generally apps use an app account system for their users to access those products and services wherever they are. That also should include logic to prevent the duplicate purchase from occurring on another platform.
Check out this article, while it's about multiple apps, the concept is the same whether that other app was the web, Google play, etc. https://developer.apple.com/documentation/storekit/offering-a-subscription-across-multiple-apps