How do you start an `SKProductsRequest` in a watchOS app, when the existing product identifiers from the iOS app use a main bundle ID?

I have a watchOS app (not independent) that I'm trying to bring StoreKit support to purchasing subscriptions. When I make my existing StoreKit manager for iOS target watchOS, the productsRequest(_:didReceive:) delegate callback returns an empty response.products array but I don't understand why.

One guess as to the cause is that when I initialize the SKProductsRequest, the products identifiers I pass ones with prepended bundle identifiers, which may different between iOS and watchOS? The existing iOS code has the format

static let subscriptionKindOne = Bundle.main.bundleIdentifier!.lowercased() + ".subscriptionKindOne"
static let subscriptionKindTwo = Bundle.main.bundleIdentifier!.lowercased() + ".subscriptionKindTwo"
static let subscriptionKindThree = Bundle.main.bundleIdentifier!.lowercased() + ".subscriptionKindThree"

Is this right? If so, what would be the correct way to start a products request on watchOS, so that the SKProductsResponse products array is populated?