How do I get he product info from the productIdentifier

The best way to easily and accurately to show the user the status of their subscription is to send them to their device’s subscription settings page using the managementURL property of the purchaserInfo. The URL will deeplink directly to your app’s subscription settings page on the device, where the user can check how much they paid, when the subscription will renew, ways to cancel, etc. It’s the most accurate representation of the user’s subscription on the device and gives the user more actions to manage their subscription than inside your app, so we highly recommend using it.

If you really want to display that info in your app, here’s where to get each piece of info:

subscription name: You can get the name of the subscription product using title property of the product. The description of the entitlement isn’t available via the SDK or REST API yet - we’re working on providing better functionality here in future iterations of our API.

purchase value: This is tricky. You can get the current price of the product by using the priceString property of the product. If they’re in an intro period you should use the introductoryPrice instead. But it’s possible that the current price of the product doesn’t match the price that the customer paid - for example if you changed the price after they purchased it, they redeemed an offer code or promo code for the product, etc. So the best option is to direct them to the device’s subscription settings for price info. Maybe include all of the other information except the price?

subscription period: You can get this from the packageType property of the package. Note that if you use custom packages then the packageType will be CUSTOM.

expirationDate: You can get this from the entitlementInfo like you said.