Unable to change Apple Account password on a new iPhone

Verification is done with the information that you had previously provided on your account. When asked for credit card verification, it makes no difference if the card is active, they are just trying to confirm that it matches what you had previously entered. To receive the call/text, it will go to the Trusted Phone numbers that have been previously entered on your account.

These are 2 methods that are used to immediately reset your password and without it, you will likely have to use Account Recovery. There is a delay in resetting the password when using Account Recovery and the instructions for doing that are here:

How to use account recovery when you can’t reset your Apple Account password - Apple Support

After you gain access to your account again, make sure to update your Trusted Phone Numbers so you will be able to receive the text/call next time.

About trusted phone numbers and trusted devices for Apple Account - Apple Support

Ok, it sounds like Apple started the Account Recovery request for you, and when viewing the previous supplied link for using Account Recovery, it states:

After you request account recovery, you get an email with a confirmation of your request and the date and time of when you can expect to regain access. This email arrives within 72 hours.

It may be several days or more before you can reset your password. Contacting Apple Support can’t help you shorten this time.

When the waiting period is over, Apple will send you a text or automated phone call with instructions to regain access to your account. If you don’t receive the text or call, once the period specified in the original email is over, you can still go directly to apple.com/recover. Follow the instructions to regain access to your Apple Account.

I would suggest to use that "recover" link provided in the Support Article. Also note that from the same Support Article, an Account Recovery request may be cancelled if any device is currently using that same Apple Account.

• Regardless of how you started the account recovery request, you should turn off all other devices that are currently signed in with your Apple Account until account recovery is complete. If your Apple Account is in use during your request, your account recovery will be cancelled automatically.

Normally when you do have a Trusted Phone number on your account that is accessible, there is no need to go through the Account Recovery process. You would follow the steps here for a forgotten password and first the verification link is sent to any Trusted Device, which is another device currently logged into your account if you have one. If you do not have one, then you choose the button that says "Didn't Get Code", where you will then have the option to send the link to one of your Trusted Phone numbers and choose which number you want that sent to.

If you forgot your Apple Account password - Apple Support

I am not sure why Apple Support directed you to Account Recovery when you do have a Trusted Phone Number on your account that is your phone number, where you should have been able to reset the password yourself using the link sent to that number. That would have eliminated the need for the waiting period, email confirmation, and credit card verification. I am afraid if you now try resetting the password again, it will cancel your previous request for Account Recovery and only delay you further.

Let us know how it goes after you use the apple.com/recover link in the Support Article. While Apple cannot speed up the Account Recovery process once submitted, they may have additional information on whether that previous request has been cancelled.

Contact Apple Support - Apple Support

From my understanding, the Apple Account that is being reset is not signed into the phone since the Password was unknown at that time. The article recommends to not use devices that are currently signed into the account as that may cancel the Account Recovery request, so you should be good there. Were you able to gain any additional insight using  apple.com/recover for when you did not get the text or phone call?

If all other options have been exhausted, you may consider the following recovery strategy:

1. Restore your iPhone from a previous backup—specifically one associated with an Apple ID for which you still remember the password.
2. After the restoration is complete, sign in using that known Apple ID.
3. Once signed in, update the Apple ID on the device to the account you are trying to recover.
4. While still signed into the account you do have access to, designate it as a recovery contact for the account you're locked out of.
5. Initiate the account recovery process for the forgotten Apple ID using the recovery contact setup.

This approach leverages the known Apple ID to assist in the recovery of the inaccessible account through Apple’s recovery contact feature

If it has been stated in an email that you’d get a message or call, but there has been none (is your current phone number really the trusted one?), respond and ask for additional assistance. It won’t be a problem, apple support is there for that kind of stuff.

According to their description, shouldn’t the account now be signed into those 2 phones though? Or am I misreading it? Fyi I’m taking this from “we’ve transferred all the data”, implying that they’ve signed in on the new device before beginning the transfer progress, because you have to when transferring data via iCloud or quick start, right?