Thanks for your answer.
I’m observing the same behaviour in the sandbox environment. Here are the steps I've done if that helps:
I created a Sandbox account in App Store Connect: I cleared the Purchase History for this tester and set the Subscription Renewal Rate to Monthly Renewal Every 3 Minutes.
I created a fake App in App Store Connect.
I configured a subscription group in App Store Connect for this fake app and added a monthly subscription to this subscription group (this monthly subscription is in Ready To Submit stage after I added enough meta data).
I run the app without using the Xcode config file: the product added to the app on App Store Connect is correctly loaded by the app and I can subscribe to it using the sandbox account on a real device.
I leave the app opened and I receive the transactions when the app is running.
I hard quit the app and wait enough time for virtual renewals to normally be created (for example I wait 30 minutes, which should have renewed the app 10 times based on the Sandbox tester account setup for subscription renewal rate).
I launch the app again and fetch the last transaction for this subscription: it's still the one downloaded 30 minutes ago, before the app was quitted.
I fear the behavior is the same in a production environment so I fear I missed anything and don’t want to ship not working subscription management in my app.