Monthly installments does not appear as an option on my Apple Card

Apple Card’s installments are for eligible purchases made at Apple. This page shows some info about it: Apple Card - Monthly Installments - Apple. Also, if you’re using a discount like the student discount or the corporate discount, the installment option probably won’t come up.

They did announce a new feature that is coming with iOS 16 where you’ll be able to split purchases up over a few weeks, but that isn’t available yet.

It isn't an option that appears on the card; it is an option that is available when checking out when making a purchase directly from Apple. See: Apple Card - Monthly Installments - Apple