This is in-game, so I've already downloaded the game but can't activate the full license without that menu disappearing and bringing me straight back to the main menu. I found a forum where others had this issue on iOS as well, but the thread had no solution.
Everything about sale is part of Google infrastructure, there was no update so its really a play store problem. Not much we can do on that site. You can try to reboot, reinstall the game, clear the cache, but that's all I can recommend you. If it still won't work, contact Google. It should work. IOS problem is something else, it's different since you use Android device.
Preferably use it with computer, not phone. When purchasing, use account you use on your phone as main account (in case you have more than one gmail account you use).
If you still have problems, then you should try get help with Google, as this is problem on their site. Game just uses Google infrastructure and calls it, within game itself (when you try to purchase from phone), as well as when you access Google Play Store.
So, we can't help you if you still have problems, as they are solely under Google's control.
While this is under Google control as explained above, there is something that 90% of the times solves this issue: Enter Play Store app, go to settings and remove your payment method data, then add it again. After that, try the purchase.
If it still fails, please make a small test: open any other app with in-app purchase and check if you can initiate a purchase. You don't have to actually buy anything, just check if you see the first "prompt window" from Google showing the price, payment methods available, etc. My guess is, it will fail with all other apps as well.