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Most manufacturers require a factory reset before sending away to be repaired. However if it's not a software fault then you are inconvenienced.
Is it possible to do a full image backup of the phone? I've read through a few of the answers here but they're a few years old.
AndroidKeyStorethen it is not possible. As far as I know cryptographic keys in that store can only be accessed/used but not exported even with root permissions (if the key has been created as non-exportable key). If you perform a factory reset the necessary keys to decrypt those keys are gone.