Is there there an iOS equivalent of Android's "Delete app storage"?

Not really - On iOS, deleting the app only deletes the data in its sandbox. If the developer doesn’t offer this toggle in the settings app (or you don’t trust the developer to actually wipe the data) you might have a problem if you expect all traces to be removed.

The problem is apps store data in a lot of places that aren’t the app sandbox. Look at keychain, cloud and application group stores for places where “data the developer really doesn’t want you to delete” can persist.

In the case where the app uses a group data entitlement, that data will persist and one app can participate in more than one group. A very notable version of this is Microsoft Office suite of iOS apps - they all share one group container so deleting an app doesn’t necessarily delete that data. Licensing and identity is stored in the group area, but individual data (Word / Excel / Outlook) is still stored within the app bundle so deleting Word, deletes the Word-specific data, but not some data relating to Office (licensing and identity and certificates for example).

So, no - sandboxing is different on iOS and there’s not an OS setting to wipe as a direct analog to how Android implements this. You’ll need to consider each app, whether it syncs to iCloud data store, to another data store or a group container to achieve your needs.