I've lost my PvZ2 account

The image shows 2 new account IDs, this generally appears if you have chosen to start a fresh game on the last re-install, in short, the original account with your old proress (which was linked to your email address) has been overwritten.  If this were the case, this might not be good news.  

You mentioned you have installed the game on many devices in past, do you by any chance still have access to one of those device which still have the game installed?  If so, you might be able to save your old progress by trying the steps below.

1. On the old device, disable internet data (WiFi & mobile data) and then start the PVZ2 App.

2. Once it starts to the main menu, click the spanner button, locate and screenshot your original player ID.

3. Back out to the main menu, enter adventure mode and then enable internet data, back out to the main menu.

4. Enter the adventure mode again and there should be option to earn gems/coins by watching ads. Watch some ads for gems or coins to increase your resources.

5. Back out to the main menu, click the cloud button, click the Force Sync Player Data button. Hopefully, this would update the latest data to your original account.

6. On your new device, delete the PVZ2 App and do a fresh install. Once the game starts to the main menu, try doing the email register and see if the original account is available from the ID conflict screen, if so, then you can recover your old progress yourself.  If not, you will need to contact EA help center and provide the screeenshot of your original ID which you have taken on your old device and get assistance to re-link your email address.

Good luck. 

2 devices where it have probably been installed don't turn on. But thanks for your advices. 
Fortunately, there was another option - I've chatted to the EA support and after few hours I've received an e-mail that they brought the account back. I just had to choose it. Now everything works well. So much stress it costed but now that's a relief. 

Thanks for the reply and sharing the good news.

Out of curiosity is your current player ID remain with one of the two IDs showing up in your post or have you got a new ID?

Probably a new one. But how can I check it? 

Click the spanner button to enter Settings from the main menu.

For iOS, select Download Preferences to see your current player ID.

For Android, select Build Version to see your current player ID

I've lost it again - it was too hot for the phone. No missclicks this time. But I cannot choose my account from the menu. Inside the cloud it is described that I've registered my account which is true but I can't see my progress. What do you think? Would reinstalling help? 
I've written to the EA Help yesterday and they told me they need my in-game ticket. What is it? How to get this? Is it the same as ID? 
There's still hope - the game can see my achievements. 

The game menu looks like this - I cannot choose the account. That's why I'm wondering if reinstalling would help. 

Suggest to try the method on link below and let us now if it helps.

(it seems to help recovering game progress for some members using Android devices)

https://www.youtube.com/watch?v=6X_EnMKZ5Zo

Thanks. Unfortunately, there's a big difference between your menu and mine: you can choose the player even before you clear the cache. That's why I'm not so sure if clearing it would help and maybe it would harm the EA's help. I'll probably wait with it for some hours.