I’m having this exact issue as well with one exception. It works on my old phone but not on my new phone and it works on my iPad still as well.
On my new phone I have tried reinstalling multiple times, logging out of Game Center, multiple different WiFi connections including home and public, 4G, LTE, another phones hot spot, and none of these works. I get the same error on all of these “connection error. Please your internet connection and try again.”
I have also tried to reinstall after removing my PvZ heroes iCloud backup. No joy still. I do have an EA account that I use to sign in and sync across devices. I have also already tried all of the connection troubleshooting steps provided by EA support in regards to this issue. None of those were successful in resolving this problem.
T