Can I use a foreign passport to set up Apple Pay?

Interesting. I never needed to do that, but I was using my bank account and credit card. The site states US documents only, so my initial answer would be no.

This does not look like Apple Pay to me, but part of the requirement for applying for an Apple Card. Is that what you are doing?

For what purpose would you want to use the passport? Apple Pay is set up using a supported credit card. See this information. Set up Apple Pay - Apple Support