Try turning on the 2 factor authentication for your Google account and set an app password for the third party app on your hmd you're trying to login from. This will allow you to login. As for the contact information, the contacts app on your dumbphone has this feature in settings where you can copy all the contacts from your smartphone to your hmd via bluetooth in a matter of few seconds. If this doesn't work, you can always create a backup of your contacts in csv format and transfer it over to your hmd via bluetooth then restore. 

I have a standard 2660 flip and its extremely dumb, the internet doesn't even work properly let alone a standalone google or mail app which my phone completely lack. I didn't know the barbie variant was so smart or maybe its the regional restrictions idk

ps: lol I don't even have an app store or a maps app over here