How to use my old Apple ID without the registered phone number on my new iPhone?

If you can still sign into your account on another device you can investigate adding more ways to get a code such as multiple telephone numbers where you can receive a text or a phone call. This is based on the section "About trusted phone numbers and trusted devices" in the article: Two-factor authentication for Apple ID - Apple Support

To see, add, or change your trusted phone numbers use one of these methods:

● On your iPhone, iPad, or iPod touch: Go to Settings > your name > Password & Security. Next to Trusted Phone Number, tap Edit.

● On a Mac computer choose Apple menu  > System Settings (or System Preferences), then click your name (or Apple ID). Click Password & Security, then add or remove a trusted phone number.

● Using a web browser:

1) Go to https://appleid.apple.com and sign in.

2) Follow security options until you find one letting you change trusted numbers,

3) Click "+" to add a new number (you may be required to verify this number).

4) If you wish to remove an old number, click "-" next to the number.

Similar information for the iPhone can be found here --> Use two-factor authentication for your Apple ID on iPhone - Apple Support

If you had set up an Account Recovery Contact ( Set up an account recovery contact - Apple Support ) you can also get a code that way.

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. This article explains how to recover your Apple ID after a waiting period - How to use account recovery when you can’t reset your Apple ID password - Apple Support One tip to using account recovery it to look for options in small blue letters beneath the normal log-in items if you cannot complete the requested information. The post by shoeluvr13 at this link provides additional detail about the account recovery process: Activation Lockout Issues - Apple Community

You should consider making sure you have multiple trusted devices and telephone numbers (ask a friend or a relative).

You may also wish to read the articles 'Two-factor authentication for Apple ID' ( Two-factor authentication for Apple ID - Apple Support ) and 'Get a verification code and sign in with two-factor authentication' ( Get a verification code and sign in with two-factor authentication - Apple Support ). Various sections contain information that is useful in understanding about the trusted devices (an iPhone, iPad, or Mac that Apple knows is yours) system, and how to get a verification code on a trusted device or at a telephone number.

You can try and and submit an account recovery request to regain access to your account How to use account recovery when you can’t reset your Apple ID password - Apple Support