Resetting Password for iCloud but now have New Phone Number.

If you are prone to forgetting passwords then I would not set up a 28 digit recovery key (Set up a recovery key for your Apple Account - Apple Support ) on that new account. Should you forget the password again (and it sounds like these people are not really up on this kind of thing) and also lose the recovery code, you will be permanently locked out of the account. Apple can do nothing to help you.

A verification code can be sent to a landline. Look for other options and it should let you get one by voice.

Based on: Get a verification code and sign in with two-factor authentication - Apple Support

A code is sent first to your trusted devices (some other Apple computer or Apple mobile device signed in with your account) automatically. If you have a trusted device running iOS 9 and later, OS X El Capitan and later, iPadOS 13 and later, or watchOS 6 and later, the verification code is displayed automatically on your trusted devices.

If you don’t have a trusted device handy, you can choose to have a verification code sent to your trusted phone number as a text message or phone call.

1. Select “Didn’t Get a Code?” or “Can’t get to your devices?” on the verification code screen.

2. Choose a telephone number for where to receive a code.

3. You'll get a text message or phone call from Apple with your verification code. This text message might include an additional domain validation line. This line includes the @ symbol, the website name, and your code (for example: @icloud.com #123456 %apple.com).

4. Enter the code on your other device to complete sign in.

It is a good idea to have more than one trusted number.

If you had set up a recovery contact, read Help a friend or family member as their account recovery contact - Apple Support

You do not mention security questions so I won't complicate this issue by posting stuff about issues you do not even mention. If you cannot get code by phone call, you may need to do as instructed here --> How to use account recovery when you can’t reset your Apple Account password - Apple Support

Age is not an issue in understanding things unless somebody is truly having dementia. Many of the top helpers on this forum are well into retirement age. Similarly, I was talking to a car guy yesterday in his thirties and he was clearly not familiar with many aspects of cars from the 1980s.

If you can't unlock your Apple ID

If you use security questions with your Apple ID, or if you don't have access to a trusted device or phone number, go to iforgot.apple.com. Then you can unlock your account with your existing password or reset your password.

Watch this GIF

What if I can't access a trusted device or do not receive a verification code?

If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign-in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device. Learn how to get a verification code.

If you use iOS 11.3 or later on your iPhone, you might not need to enter a verification code. In some cases, your trusted phone number can be automatically verified in the background on your iPhone. It’s one less thing to do, and your account is still protected with two-factor authentication.

If you lost / can't reach the trusted device or phone number associated with your Apple ID

As long as you still have your Recovery Key and remember your Apple ID password, you can sign in and add a new trusted device or phone number to your account. You can also remove any devices you may have lost, sold, or given away.

1. Go to your Apple ID account page and enter your Apple ID and password.
2. On the Verify Your Identity screen, select "Can’t access your trusted devices?"
3. In the pop-up window, enter your Recovery Key.
4. Go to the Security section and click Edit.

Remove the device you no longer wish to use to verify your identity. If you have additional devices with Find My iPhone enabled, you can verify them as trusted devices. You can also add additional trusted phone numbers.

If you lost your Recovery Key

As long as you remember your Apple ID password and still have access to one of your trusted devices, you can sign in and create a new Recovery Key.

1. Go to your Apple ID account page.
2. Sign in with your password and trusted device.
3. In the Security section, click Edit > Replace Lost Key.

Keep your new Recovery Key in a safe place. Your old Recovery Key won't work anymore and you can't use it to reset your password or access your account.

If I can't sign in, how do I regain access to my account?

If you can’t sign in, access a trusted device, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery is an automatic process designed to get you back into your account as quickly as possible while denying access to anyone who might be pretending to be you. It might take a few days—or longer—depending on what specific account information you can provide to verify your identity. If you can't sign in with two-step verification using your Apple ID ...

Do I still need to remember any security questions?

No. With two-factor authentication, you don't need to remember any security questions. We verify your identity exclusively using your password and verification codes sent to your trusted devices and phone numbers. When you enroll in two-factor authentication, we keep your old security questions on file for two weeks in case you need to return your account to its previous security settings. After that, they're deleted.

Can Apple Support help me regain access to my account?

Apple Support can answer your questions about the account recovery process, but can't verify your identity or expedite the process in any way.