Sorry to hear your Spotify Subscriptions gone for a walk about, but I'm sure we can get this sorted :)
If you make sure you log in with the same Spotify account on your phone, the same as your old phone, you should still have your Spotify Subscription.
To make sure your Spotify Subscription didn't run out, you can visit spotify.com/account and sign in, if it say's your on Free, if you go to spotify.com/account/receipts it'll tell you when your last payment was (if it was more than a month ago, your subscription has most likely expired).
I am having exactly the same problem. I have just bought an iPhone 7 and have downloaded the app, logged in and it says I'm on a free subscription. I've been onto the pages you suggested and it is saying that I have a free account. When I check receipts it says that there are none. Yet I have just checked my own bank account and the last Spotify premium payment went out on the 15th May. Please could you help?