Getting back on topic it seems that you have fallen foul of one of the security demons protecting the information accessed via your Apple ID. Apple does take security of user information pretty seriously and has automated procedures intended to prevent an unauthorised user taking control of your Apple ID and thereby getting access to your data.
I presume it interpreted transfer to the new phone as being an attempted hijack and blocked the account. Presumably with both phones being close together the system assumed that your original phone had been stolen so a nefarious person could be assumed to have control of both phones.
If you have an Apple computer with access to the same ID it should either still work, so verifying that the ID still exists and is live, or at least provide the independent verification needed to re-construct access. Which, as I understand it, is deliberately made not easy. If the ID is just on the phone it may well be gone for good, along with your data. There are some triggers for an automatic block / wiping of the ID which simply cannot be unwound. Especially if your data is encrypted.
Most likely I think if the new phone has the "secure enclave" and the old one didn't. Secure enclave is supposed to make it easier to handle secure data and to verify that the owner is in control of the phone but it demands pretty careful following of the procedure. I'd not care to go from a non secure enclave phone to one with it via the automated procedure. Too much potential for hard fails. I'd certainly not care to do so for a second hand phone where you cannot be sure that the secure enclave has been properly cleared and re-virginised.
You just have to hope that your local experts haven't made a major error and locked everything down. Usually Apple provides a way back for typical "inadvertent customer" type errors.
Fingers crossed.
Clive