If I backup my iPad that is signed in my google account, and then I'm restoring it on a new iPad, will my google account transfer aswell?

Haiii,

You may backup your iPad on an iCloud Drive, but more directly, directly transfer your information to the new device using Quick Start(a built in function that will enable on the new device).

Use Quick Start to transfer data to a new iPhone or iPad - Apple Support

Through that guide, you will be able to select “transfer your data” directly during the booting phase of your new device.

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As for the Google Account, we usually use AppleID here for the main purpose of signing into applications and iCloud backups. If it is a third party account and not for the AppleID, it is not used directly for backing up a device.

As far as I know, the core data associated with the Google app—such as your search history, preferences, and other account-related content—is stored online in Google’s cloud and tied to your Google Account, not locally on your iPad. Therefore you should be able to access it when you login back in another device without needing to backing up the local copy of the google app(make sure everything inside is synced). But since it is not working on the iPadOS 12, try to login from another device first to check that everything is synced and up to date before deleting or removing anything from any of the devices.

An Apple ID backup (via iCloud or a computer) is not required to restore your Google Account data but is necessary to transfer the Google app’s presence, other apps, and device settings.

If it is still not working, you might need to contact the customer support of the respective application that is using the Google Account for more direct assistance.

Hope that helps ;w;