Should I provide my Social Security Number for Apple Pay?

See the following from Legal - Apple Cash and Apple Payments Inc. & Privacy- Apple

Verifying Your Identity

You may be asked to provide information, including your name, address, and Social Security number, to the bank and their identity verification service provider to verify your identity and to comply with banking regulations. Information you provide to verify your identity will be used only for fraud prevention and to comply with United States financial regulations. Your name and address are securely stored by the partner bank and Apple Payments Inc. If needed to verify your identity, you may be asked to provide additional information, such as date of birth, answers to questions (for example, confirming a street name you have previously lived on), or a copy of your government ID. This additional information cannot be read by Apple Inc.

Not Apple Pay, but rather Apple Cash.

Why is positive ID required?

The Patriot Act requires that lenders, banks etc obtain a confirmed ID.

“To help the government fight the funding of terrorism and money laundering activities, Federal law requires all financial institutions to obtain, verify, and record information that identifies each person who opens an account. What this means for you: When you open an account, we will ask for your name, address, date of birth, and other information that will allow us to identify you. We may also ask to see your driver's license or other identifying documents.”

Identity verification for Apple Card or Apple Cash