Agreed, this could be a mass scripted attack. Happened to me around 9:30AM Pacific Time. This however could be an issue that Apple is experiencing with one of their services as well... Haven't called yet to verify, but seeing all of these reports of correlated experiences and no official response from Apple is somewhat unsettling.
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Yes, it is possible for an attacker to spoof your SIM card/phone number, attempt a password reset and have a 2-factor auth code sent to the attacker's device. This is called SIM swapping (
https://en.wikipedia.org/wiki/SIM_swap_scam).
Good thing you changed your password. When changing you should have been asked to log out of all devices currently logged into your iCloud account - make sure you do log out of all devices using this feature if you didn't do that the first time around.