Already subscribed, but I only get the “Start Playing” button. It won’t let me actually download any games.

I never get the option to download a game. All I ever see is the “Start Playing” button. Once I click that, it just confirms that I’m subscribed and tells me when my subscription will expire. I made sure everything is up to date and closed and re-opened the App Store. Still only ever see the “Start Playing” button. Never the “Get” or download buttons.