Different email for iCloud and Apple Card—how to add to Wallet?

Note: I searched and found a post from 2022 regarding this issue, but the reply was unhelpful.

I applied and was approved for an Apple Card using a different Apple account than the one I use for iCloud on my phone (iPhone 17 Pro, if relevant). As it stands, I am unable to add the card in Wallet, and therefore I'm unable to even request a physical card.

When I attempt to add the card in Wallet, I am only shown the option to apply under the email I use for iCloud. There is no option to access Apple cards under other Apple accounts. Signing out of my iCloud account and into the other account isn't helpful since the card wouldn't display in my Wallet after signing back in with my iCloud account, anyway.

This makes my card essentially useless. Please help. Also, I am not asking how to merge accounts; I realize that isn't an option (and wouldn't want to, anyway).