iCloud account recovery with forgotten password and no old number.

You must start the account recovery process in order to regain access to your account

https://support.apple.com/en-us/118574

Is there a button offering other options?

If you are signed into this forum using the same Apple Account then your browser may be configured to automatically enter your password. You should be able to view stored passwords in your browser's preferences/settings.

This Apple article has instructions for what to do if you have forgotten your Apple account password, or the system does not recognize the one you remember —> https://support.apple.com/102656 or go directly to this web reset link —> https://iforgot.apple.com/ (“The reset process on the web might take a little longer. If you’ll have access to one of your trusted devices soon, it might be faster and easier to reset your password at that time.”)

If you find you can’t sign in, reset your password, or receive verification codes, you can request account recovery (read this support article: https://support.apple.com/102656#:~:text=If%20you%20can%27t%20reset%20your%20password%2C%20request%20account%20recovery ) to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. This is a multi-step process. More detail in —> https://discussions.apple.com/thread/255401538?answerId=260044580022#260044580022 and https://discussions.apple.com/thread/255733423

This page has telephone numbers for contacting Apple for support and service ➞ https://support.apple.com/106932